C₂²×#2365 #7625373

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

Aliases

12018 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂²×#59051, C₂²×#39146, C₂²×#36115, …
maximal normal subgroup of	C₂²×#59051, C₂²×#39146, C₂²×#36115, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532569);