C₄×#1279 #105352

order	512
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

1286 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)(17,18,20,23,21,24,19,22);(6,8)(9,10,12,15,13,16,11,14)(18,22,24,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 12548);