C₄×#1943 #354658

order	512
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1390 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₄×#23029
maximal normal subgroup of	C₄×#23029

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261854);