C₃²×Q₈×C₂₃ #13110269

order	1656
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

C₃²×Q₈×C₂₃

	subgroup	G/H
center, socle, prime radical	C₂×C₃²×C₂₃	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃²×C₂₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₂₃ ◁ G

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1656

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3)(7,8,9,10)(11,14,13,12)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(4,5,6)(7,11,9,13)(8,12,10,14)

1035 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1656, 107);