C₂²×C₁₁×#525 #14639852

order	2816
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₁ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂²×C₁₁×#525

	subgroup	G/H
center	C₂³×C₄×C₁₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
socle	C₂⁴×C₁₁	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁ ◁ G

14334 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 27 points:

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

1232 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55647);