C₂⁴×C₃²×C₈ #11770618

order	1152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 990904320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂⁴×C₃²×C₈

5928 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 5 generators on 22 points:

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

1152 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4629);