C₄×#1870 #354185

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2642 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);(6,8)(9,10)(11,12)(13,14,17,19,16,15,18,20);(5,6,7,8)(13,15,17,20,16,14,18,19);(10,12)(14,15)(19,20)

maximal subgroup of	C₄×#23860, C₄×#20898
maximal normal subgroup of	C₄×#23860, C₄×#20898

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261381);