#72209636

order	9720
isoclinism	isoclinic class of #72209636
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#72209609
commutator, hypocenter	G	C₁
Frattini, Fitting, socle, cosocle	C₂×C₃⁴	A₅
LCS	G
UCS	C₁ ◁ C₂

97 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,31)(28,32)(29,33)(30,37)(34,43)(35,41)(36,42)(38,46)(39,45)(40,49)(44,54)(47,53)(48,56)(50,59)(51,60)(52,61)(55,64)(57,65)(58,68)(62,70)(63,73)(66,77)(67,78)(69,72)(71,79)(74,75)(76,82)(80,83)(81,84);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(26,29,34,31,35,38,32,36,30)(33,39,40)(37,44,53,43,52,56,46,55,45)(41,47,50)(42,48,51)(49,57,58)(54,62,71,61,68,74,64,72,63)(59,66,69)(60,67,70)(65,75,81,77,73,80,78,79,76)(82,83,84);(25,27,28)(30,34,38)(33,41,42)(37,43,46)(39,47,48)(44,52,55)(54,61,64)(57,66,67)(58,69,70)(63,71,74)(73,79,75)(82,84,83);(25,27,28)(26,31,32)(39,47,48)(40,50,51)(44,52,55)(45,53,56)(49,59,60)(54,61,64)(58,69,70)(62,68,72)(76,81,80)(82,84,83);(25,27,28)(29,35,36)(33,41,42)(37,43,46)(40,50,51)(45,53,56)(49,59,60)(57,66,67)(62,68,72)(63,71,74)(65,77,78)(82,84,83);(26,31,32)(29,35,36)(30,34,38)(37,43,46)(44,52,55)(45,53,56)(54,61,64)(62,68,72)(63,71,74)(65,77,78)(73,79,75)(76,81,80)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

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

gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,31)(28,32)(29,33)(30,37)(34,43)(35,41)(36,42)(38,46)(39,45)(40,49)(44,54)(47,53)(48,56)(50,59)(51,60)(52,61)(55,64)(57,65)(58,68)(62,70)(63,73)(66,77)(67,78)(69,72)(71,79)(74,75)(76,82)(80,83)(81,84), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(26,29,34,31,35,38,32,36,30)(33,39,40)(37,44,53,43,52,56,46,55,45)(41,47,50)(42,48,51)(49,57,58)(54,62,71,61,68,74,64,72,63)(59,66,69)(60,67,70)(65,75,81,77,73,80,78,79,76)(82,83,84), (25,27,28)(30,34,38)(33,41,42)(37,43,46)(39,47,48)(44,52,55)(54,61,64)(57,66,67)(58,69,70)(63,71,74)(73,79,75)(82,84,83), (25,27,28)(26,31,32)(39,47,48)(40,50,51)(44,52,55)(45,53,56)(49,59,60)(54,61,64)(58,69,70)(62,68,72)(76,81,80)(82,84,83), (25,27,28)(29,35,36)(33,41,42)(37,43,46)(40,50,51)(45,53,56)(49,59,60)(57,66,67)(62,68,72)(63,71,74)(65,77,78)(82,84,83), (26,31,32)(29,35,36)(30,34,38)(37,43,46)(44,52,55)(45,53,56)(54,61,64)(62,68,72)(63,71,74)(65,77,78)(73,79,75)(76,81,80));