C₄×#1296 #105448

order	512
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

1042 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 512

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 12644);