C₂×C₄×C₈² #180781

order	512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 50331648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄²×C₈

Aliases

C₂×C₄×C₈²

1922 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 87977);