C₂×C₃⁴×C₈ #13049166

order	1296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 388177920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃⁶

Aliases

C₂×C₃⁴×C₈

2332 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 4 generators on 22 points:

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

1296 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2884);