C₄×#2054 #359110

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2004 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)(14,19)(15,20)(16,17);(9,10)(11,12)(13,14)(15,16)(17,19)(18,20);(6,8)(10,12)(13,15,16,14,18,19,17,20)

maximal subgroup of	C₄×#24267, #72322660, #72322667, …
maximal normal subgroup of	C₄×#24267, #72322660, #72322667, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266306);