C₃³×C₄×C₁₁ #11924704

order	1188
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 224640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₄×C₁₁

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1188

A minimal faithful permutation representation — 3 generators on 24 points:

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

1188 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 74);