C₂²×C₁₁×#500 #14637847

order	2816
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂²×C₁₁×#500

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

2398 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 5 generators on 31 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 53642);