C₄³×C₈ #353104

order	512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1409286144
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄⁶

Aliases

C₄³×C₈

3330 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260300);