Group #72209675

(2,4,3,5)(6,22,11,23)(7,27,12,28)(8,18,13,21)(9,14,15,10)(16,30,19,44)(17,56,20,57)(24,61,41,67)(25,34,37,47)(26,55,42,63)(29,58,43,65)(31,78,45,79)(32,54,46,62)(33,51,48,40)(35,89,52,69)(36,71,53,93)(38,96,49,80)(39,98,50,87)(59,68,64,75)(60,103,66,82)(70,88,85,105)(72,110,95,92)(73,108,90,100)(74,112,102,116)(76,115,91,117)(77,106,99,84)(81,111,83,94)(86,121,104,118)(97,120,107,119)(101,114,109,113);(2,6,7)(3,11,12)(4,16,17)(5,19,20)(8,31,32)(9,35,36)(10,38,39)(13,45,46)(14,49,50)(15,52,53)(18,27,61)(21,28,67)(22,66,55)(23,60,63)(24,68,43)(25,72,58)(26,73,64)(29,41,75)(30,54,77)(33,83,84)(34,86,87)(37,95,65)(40,91,80)(42,90,59)(44,62,99)(47,104,98)(48,81,106)(51,76,96)(56,97,113)(57,107,114)(69,88,102)(70,118,108)(71,119,111)(74,89,105)(78,110,115)(79,92,117)(82,109,116)(85,121,100)(93,120,94)(101,112,103);(1,2,8,28,16,54,62,19,27,13,3)(4,9,33,65,20,64,116,63,23,47,14)(5,10,34,22,55,112,59,17,58,48,15)(6,12,43,91,35,90,97,38,95,69,24)(7,11,41,89,72,49,107,73,52,76,29)(18,37,85,117,66,79,94,36,67,105,51)(21,40,88,61,53,111,78,60,115,70,25)(26,44,56,103,92,87,113,77,50,108,71)(30,42,93,100,39,99,114,98,110,82,57)(31,75,46,102,83,120,101,86,121,84,80)(32,68,45,96,106,118,104,109,119,81,74);(1,4,18,7,30,46,32,44,12,21,5)(2,9,37,11,42,102,68,56,43,40,10)(3,14,51,29,57,75,74,26,6,25,15)(8,33,85,41,93,83,45,103,91,88,34)(13,47,105,76,82,31,81,71,24,70,48)(16,20,66,72,39,101,106,87,90,53,55)(17,19,63,36,73,98,84,109,50,95,60)(22,28,65,117,89,100,120,96,92,35,61)(23,67,52,110,80,119,108,69,115,58,27)(38,78,59,62,116,94,107,114,121,104,77)(49,99,86,118,113,97,111,112,54,64,79)

Conjugacy classes & character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀
size	1	120	121	1452	1452	1452	1452	2420	2420	3630
order	1	11	2	5	5	10	10	3	6	4
χ₁	1	1	1	1	1	1	1	1	1	1
χ₂	2	2	-2	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	-1	1	0
χ₃	2	2	-2	$\frac{- 1 - \sqrt{5}}{2}$	$\frac{- 1 + \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	-1	1	0
χ₄	3	3	3	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	0	0	-1
χ₅	3	3	3	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	$\frac{1 + \sqrt{5}}{2}$	$\frac{1 - \sqrt{5}}{2}$	0	0	-1
χ₆	4	4	4	-1	-1	-1	-1	1	1	0
χ₇	4	4	-4	-1	-1	1	1	1	-1	0
χ₈	5	5	5	0	0	0	0	-1	-1	1
χ₉	6	6	-6	1	1	-1	-1	0	0	0
χ₁₀	120	-1	0	0	0	0	0	0	0	0

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((2,4,3,5)(6,22,11,23)(7,27,12,28)(8,18,13,21)(9,14,15,10)(16,30,19,44)(17,56,20,57)(24,61,41,67)(25,34,37,47)(26,55,42,63)(29,58,43,65)(31,78,45,79)(32,54,46,62)(33,51,48,40)(35,89,52,69)(36,71,53,93)(38,96,49,80)(39,98,50,87)(59,68,64,75)(60,103,66,82)(70,88,85,105)(72,110,95,92)(73,108,90,100)(74,112,102,116)(76,115,91,117)(77,106,99,84)(81,111,83,94)(86,121,104,118)(97,120,107,119)(101,114,109,113), (2,6,7)(3,11,12)(4,16,17)(5,19,20)(8,31,32)(9,35,36)(10,38,39)(13,45,46)(14,49,50)(15,52,53)(18,27,61)(21,28,67)(22,66,55)(23,60,63)(24,68,43)(25,72,58)(26,73,64)(29,41,75)(30,54,77)(33,83,84)(34,86,87)(37,95,65)(40,91,80)(42,90,59)(44,62,99)(47,104,98)(48,81,106)(51,76,96)(56,97,113)(57,107,114)(69,88,102)(70,118,108)(71,119,111)(74,89,105)(78,110,115)(79,92,117)(82,109,116)(85,121,100)(93,120,94)(101,112,103), (1,2,8,28,16,54,62,19,27,13,3)(4,9,33,65,20,64,116,63,23,47,14)(5,10,34,22,55,112,59,17,58,48,15)(6,12,43,91,35,90,97,38,95,69,24)(7,11,41,89,72,49,107,73,52,76,29)(18,37,85,117,66,79,94,36,67,105,51)(21,40,88,61,53,111,78,60,115,70,25)(26,44,56,103,92,87,113,77,50,108,71)(30,42,93,100,39,99,114,98,110,82,57)(31,75,46,102,83,120,101,86,121,84,80)(32,68,45,96,106,118,104,109,119,81,74), (1,4,18,7,30,46,32,44,12,21,5)(2,9,37,11,42,102,68,56,43,40,10)(3,14,51,29,57,75,74,26,6,25,15)(8,33,85,41,93,83,45,103,91,88,34)(13,47,105,76,82,31,81,71,24,70,48)(16,20,66,72,39,101,106,87,90,53,55)(17,19,63,36,73,98,84,109,50,95,60)(22,28,65,117,89,100,120,96,92,35,61)(23,67,52,110,80,119,108,69,115,58,27)(38,78,59,62,116,94,107,114,121,104,77)(49,99,86,118,113,97,111,112,54,64,79));

order	14520
isoclinism	isoclinic class of #72209675
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₁₁

#72209675

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

GAP