C₄×#1877 #354253

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2492 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)(13,14,16,18,17,20,15,19);(5,6,7,8)(14,18)(15,16)(19,20);(10,12)(14,18)(15,16)(19,20)

maximal subgroup of	C₄×#23860, C₄×#20925, C₄×#23849
maximal normal subgroup of	C₄×#23860, C₄×#20925, C₄×#23849

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261449);