C₄×#1895 #354201

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

Aliases

2490 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)(7,8)(9,10,11,12)(14,17)(15,18)(19,20);(10,12)(13,14,18,20,16,19,15,17);(6,8)(14,19)(17,20)

maximal subgroup of	C₄×#23860, C₄×#20973
maximal normal subgroup of	C₄×#23860, C₄×#20973

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261397);