C₃²×C₈×C₁₆ #11768359

order	1152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 98304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₈

Aliases

C₃²×C₈×C₁₆

312 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 2 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2370);