C₂²×#2362 #7625364

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

12642 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 20 points:

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

maximal subgroup of	C₂²×#37786, C₂²×#34292, C₂²×#35808, …
maximal normal subgroup of	C₂²×#37786, C₂²×#34292, C₂²×#35808, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532560);