C₄×#3373 #6384560

order	512
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2168 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 20 points:

(1,2,3,4);(6,9)(10,11)(13,14,17,20)(15,18,16,19);(5,6,8,9)(7,11,12,10)(13,15,17,16)(14,18,20,19);(14,19)(15,16)(18,20);(5,7,8,12)(6,10,9,11)

maximal subgroup of	C₄×#61451, #72279856, #72279938, …
maximal normal subgroup of	C₄×#61451, #72279856, #72279938, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6291756);