#72209682

order	15000
isoclinism	isoclinic class of #72209682
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₅

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#72209620
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂×C₅³	A₅
LCS	G
UCS	C₁ ◁ C₂

100 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)(27,32)(28,30)(29,31)(33,41)(34,42)(35,37)(36,38)(43,53)(44,54)(45,46)(47,48)(49,50)(51,52);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,33,30)(29,34,31)(32,39,40)(35,43,37)(36,44,38)(41,46,49)(42,45,50)(47,51,53)(48,52,54);(25,28,35,36,29)(27,33,43,44,34)(32,41,53,54,42)(39,45,48,47,46)(40,49,51,52,50);(27,33,43,44,34)(32,42,54,53,41)(39,47,45,46,48)(40,51,50,49,52);(26,30,37,38,31)(27,33,43,44,34)(32,41,53,54,42)(39,46,47,48,45)(40,50,52,51,49)

Conjugacy classes & character table

49 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)(27,32)(28,30)(29,31)(33,41)(34,42)(35,37)(36,38)(43,53)(44,54)(45,46)(47,48)(49,50)(51,52), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,33,30)(29,34,31)(32,39,40)(35,43,37)(36,44,38)(41,46,49)(42,45,50)(47,51,53)(48,52,54), (25,28,35,36,29)(27,33,43,44,34)(32,41,53,54,42)(39,45,48,47,46)(40,49,51,52,50), (27,33,43,44,34)(32,42,54,53,41)(39,47,45,46,48)(40,51,50,49,52), (26,30,37,38,31)(27,33,43,44,34)(32,41,53,54,42)(39,46,47,48,45)(40,50,52,51,49));