C₁₁×#24424 #14601617

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23848
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁷

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 ◁ C₂×C₄×D₄×C₁₁ ◁ G

1992 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 704

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 17412);