C₄×#2014 #359037

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

Aliases

2678 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)(13,14,17,20)(15,18,16,19);(6,8)(9,10)(11,12)(14,18)(15,16)(19,20);(10,12)(14,19)(15,16)(18,20)

maximal subgroup of	C₄×#23860, C₄×#23430, C₄×#23849
maximal normal subgroup of	C₄×#23860, C₄×#23430, C₄×#23849

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266233);