C₁₁×#34681 #14611874

order	2816
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

3700 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 27669);