C₂⁴×C₄²×C₁₁ #14639831

order	2816
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1268357529600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₄²×C₁₁

24030 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 2816

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

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

2816 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55626);