C₄×#2443 #514836

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4396 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 20 points:

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

maximal subgroup of	C₄×#36096, #72306259, #72306261
maximal normal subgroup of	C₄×#36096, #72306259, #72306261

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422032);