C₃×#11761914 #72228891

order	3240
isoclinism	isoclinic class of #11761914
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Fitting, socle, hypercenter	C₃²	A₆
commutator, hypocenter	#11761914	C₃
Frattini, cosocle	C₃	C₃×A₆
LCS	G ▷ #11761914
UCS	C₁ ◁ C₃²

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 21 points:

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

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

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