C₄×#3366 #6384557

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

Aliases

2224 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)(14,17)(15,19)(18,20);(5,6,8,9)(7,11,12,10)(14,18)(17,20);(13,14)(15,20)(16,18)(17,19);(5,7,8,12)(6,10,9,11)

maximal subgroup of	C₄×#61451, #72279809, #72279975, …
maximal normal subgroup of	C₄×#61451, #72279809, #72279975, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6291753);