C₁₁×#24230 #14601423

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23876
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

1624 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 17218);