C₄×#1525 #182691

order	512
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂³×C₄²

Aliases

1580 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 20 points:

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

maximal subgroup of	C₄×#8440, #72239496
maximal normal subgroup of	C₄×#8440, #72239496

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89887);