C₁₁×#24726 #14601919

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23848
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

1222 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17,18,19);(12,13,15,14)(20,21)(22,24)(23,26)(25,27);(17,19)(21,24)(22,27)(25,26);(12,14,15,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 17714);