C₂²×#1968 #6371983

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

6378 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);(6,8)(9,10,11,12)(14,19)(15,20)(16,17);(5,6,7,8)(10,12)(13,14,16,19,18,20,17,15);(13,15,17,20,18,19,16,14)

maximal subgroup of	C₂²×#22874, C₂²×#21701, C₂²×#23022, …
maximal normal subgroup of	C₂²×#22874, C₂²×#21701, C₂²×#23022, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279179);