C₂³×C₄³ #7625197

order	512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3788161155072
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₄³

Aliases

C₂³×C₄³

33858 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 6 generators on 18 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532393);