C₅×#11761914 #72228905

order	5400
isoclinism	isoclinic class of #11761914
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Fitting, socle, hypercenter	C₃×C₅	A₆
commutator, hypocenter	#11761914	C₅
Frattini, cosocle	C₃	C₅×A₆
LCS	G ▷ #11761914
UCS	C₁ ◁ C₃×C₅

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 90

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5)(6,9,10,12,8,7)(11,14,13)(15,19,16,21,17,23)(18,22,20);(6,8,10)(7,16,19,18,11,9,17,21,20,13,12,15,23,22,14)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3,4,5)(6,9,10,12,8,7)(11,14,13)(15,19,16,21,17,23)(18,22,20), (6,8,10)(7,16,19,18,11,9,17,21,20,13,12,15,23,22,14));