C₄×#3384 #6385090

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

Aliases

2130 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);(5,6,9,8)(7,11,12,10)(14,17)(15,19)(18,20);(5,7,9,12)(6,10,8,11)(14,18)(17,20);(13,14)(15,20)(16,18)(17,19);(5,8,9,6)(7,10,12,11)

maximal subgroup of	C₄×#61451, #72279828, #72279848, …
maximal normal subgroup of	C₄×#61451, #72279828, #72279848, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6292286);