C₃³×C₇×C₈ #13094539

order	1512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 269568
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₇×C₈

224 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1512

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

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

1512 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 436);