#Number of QC classes: #A_n: 1 #B_n: 1 #D_n: Floor(n/2); #E_6: 3 #E_7: 5 #E_8: 9 #F_4: 2 #G_2: 1 #H_3: 3 #H_4: 11 ######## Conjugacy Classes H_3 (Representatives as reduced reflection decompositions) ####### 1) [ (1,3)(4,5)(6,7), (1,5)(2,4)(6,7), (1,5)(3,4)(6,7) ] 2) [ (2,3)(4,5)(6,7), (2,4)(3,5)(6,7), (1,2)(4,5)(6,7) ] 3) [ (2,3)(4,5)(6,7), (2,4)(3,5)(6,7), (1,2)(3,4)(6,7) ] ######## Conjugacy Classes H_4 (Representatives as reduced reflection decompositions) ####### 1) [ (1,2)(3,4)(5,7)(8,11)(10,14)(12,16)(15,19)(17,22)(20,26)(21,27)(23,30)(28,34)(29,35)(33,41)(36,43)(37,44)(38,47)(40,49)(42,51)(45,53)(46,56)(48, 58)(52,61)(54,64)(55,65)(59,69)(62,72)(63,74)(66,77)(68,80)(70,82)(73,85)(75,87)(76,89)(78,91)(81,93)(83,96)(86,97)(88,98)(90,99)(92,102)(94, 104)(95,105)(100,108)(101,109)(106,112)(107,114)(110,115)(113,117)(119,120), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24, 28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45,55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67, 78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93,103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27,34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47, 56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71,79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92, 100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26, 30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44,53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67, 79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91,102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115) ] 2) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (1,4)(3,6)(5,14)(8,19)(9,16)(10,18)(12,27)(13,22)(15,25)(17,35)(20,41)(23,47)(24,34)(28,51)(31,43)(32,49)(33,50)(36,61)(37,64)(38,57)(39,58)(40, 69)(44,56)(45,74)(46,77)(48,80)(53,65)(54,87)(55,89)(60,82)(62,84)(63,97)(66,75)(67,91)(70,105)(71,96)(72,85)(76,86)(78,109)(79,102)(81,103)(83, 112)(88,114)(92,115)(93,99)(94,111)(104,108)(107,118)(113,120)(116,117), (1,5)(2,9)(3,12)(4,24)(6,28)(8,20)(11,32)(13,37)(14,34)(15,40)(17,46)(18, 42)(19,60)(22,67)(25,70)(27,51)(29,78)(30,44)(31,81)(35,88)(36,90)(38,54)(39,62)(41,82)(43,86)(47,98)(48,73)(50,95)(52,74)(53,72)(57,107)(58,97)(63, 84)(64,91)(65,93)(68,89)(69,105)(71,110)(75,101)(76,103)(77,114)(79,113)(83,102)(85,99)(87,118)(92,116)(104,117)(108,115)(111,119)(112,120) ] 3) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,4)(3,6)(5,14)(8,19)(9,16)(10,18)(12,27)(13,22)(15,25)(17,35)(20, 41)(23,47)(24,34)(28,51)(31,43)(32,49)(33,50)(36,61)(37,64)(38,57)(39,58)(40,69)(44,56)(45,74)(46,77)(48,80)(53,65)(54,87)(55,89)(60,82)(62,84)(63, 97)(66,75)(67,91)(70,105)(71,96)(72,85)(76,86)(78,109)(79,102)(81,103)(83,112)(88,114)(92,115)(93,99)(94,111)(104,108)(107,118)(113,120)(116,117) ] 4) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,27)(2,14)(3,18)(5,51)(7,16)(8,69)(9,34)(10,21)(11,41)(12,42)(13, 77)(15,50)(17,87)(20,105)(22,47)(23,109)(26,49)(29,57)(30,64)(31,73)(32,82)(33,59)(36,62)(37,114)(38,75)(39,90)(40,95)(43,89)(44,91)(46,118)(48, 81)(52,97)(53,103)(54,101)(58,74)(61,80)(63,93)(65,84)(67,98)(68,86)(71,117)(72,76)(78,107)(83,119)(94,106)(96,100)(102,111)(104,110)(108,120)(112, 115) ] 5) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,34)(2,16)(3,51)(4,14)(5,24)(6,27)(8,82)(10,42)(11,49)(12,28)(13, 91)(15,105)(17,114)(19,41)(20,60)(22,64)(23,98)(25,69)(29,109)(30,56)(31,76)(33,95)(35,77)(37,67)(38,118)(39,63)(40,70)(43,103)(45,52)(46,88)(53, 99)(54,107)(55,68)(57,87)(58,84)(61,90)(62,97)(65,85)(66,101)(72,93)(73,80)(79,112)(81,86)(83,113)(92,104)(94,119)(96,110)(102,120)(108,116)(115, 117) ] 6) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,69)(2,59)(3,49)(4,40)(5,99)(6,32)(7,90)(8,88)(10,81)(11,98)(13,71)(14, 93)(15,107)(17,83)(18,103)(19,114)(20,120)(22,96)(23,51)(24,57)(25,118)(26,119)(28,47)(29,106)(30,42)(33,117)(34,38)(35,112)(37,89)(39,79)(41, 113)(44,76)(45,75)(46,97)(48,92)(50,116)(53,87)(54,65)(55,64)(56,86)(58,102)(60,84)(62,82)(63,77)(66,74)(68,110)(70,72)(73,95)(80,115)(85,105) ] 7) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,82)(2,70)(3,89)(4,76)(5,41)(7,33)(8,75)(9,25)(11,87)(12,68)(13,79)(15, 120)(16,80)(17,51)(18,67)(19,119)(20,101)(21,56)(22,42)(23,94)(24,103)(26,109)(27,46)(29,99)(30,104)(31,71)(32,118)(35,90)(36,88)(37,113)(38,97)(40, 112)(43,98)(44,117)(47,86)(48,64)(49,106)(50,84)(52,69)(54,58)(55,100)(59,61)(60,111)(63,95)(65,108)(73,91)(74,105)(78,85)(81,110)(93,115) ] 8) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 79)(74,85)(75,88)(76,90)(77,91)(80,93)(83,94)(87,98)(89,99)(92,100)(96,104)(101,107)(102,108)(106,113)(109,114)(111,116)(112,117), (2,3)(4,6)(7,10)(9,12)(11,15)(13,17)(14,18)(16,21)(19,25)(22,29)(24,28)(26,33)(30,38)(31,36)(32,40)(34,42)(37,46)(39,48)(41,50)(43,52)(44,54)(45, 55)(47,57)(49,59)(53,63)(56,66)(58,68)(60,70)(62,73)(64,75)(65,76)(67,78)(71,83)(72,84)(74,86)(77,87)(79,92)(81,90)(82,95)(89,97)(91,101)(93, 103)(94,100)(96,106)(98,107)(102,110)(104,111)(113,116)(114,118)(117,119), (1,109)(2,101)(3,91)(4,78)(6,67)(8,99)(9,84)(11,90)(12,72)(13,60)(15, 81)(16,62)(17,70)(19,93)(20,51)(21,73)(22,82)(24,50)(25,103)(26,42)(27,85)(28,41)(29,95)(31,116)(32,79)(33,34)(35,105)(36,113)(37,65)(40,92)(43, 117)(44,55)(45,54)(46,76)(49,102)(52,119)(53,64)(56,89)(59,110)(61,120)(63,75)(66,97)(69,115)(74,87)(77,86)(88,108)(94,107)(98,100)(104,114)(111, 118) ] 9) [ (5,8)(7,11)(9,13)(10,15)(12,17)(14,19)(16,22)(18,25)(20,23)(21,29)(24,31)(26,30)(27,35)(28,36)(32,39)(33,38)(34,43)(37,45)(40,48)(41,47)(42,52)(44, 53)(46,55)(49,58)(50,57)(51,61)(54,63)(56,65)(59,68)(60,71)(64,74)(66,76)(67,79)(69,80)(70,83)(75,86)(77,89)(78,92)(81,94)(82,96)(87,97)(90,100)(91, 102)(93,104)(95,106)(99,108)(101,110)(103,111)(105,112)(109,115), (3,5)(4,7)(6,9)(10,12)(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,30)(25,32)(27, 34)(29,37)(31,39)(33,40)(35,44)(36,45)(38,46)(41,49)(43,53)(47,56)(48,55)(50,60)(52,62)(57,67)(58,65)(59,70)(61,72)(63,73)(66,78)(68,81)(69,82)(71, 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