C₂²×#1925 #6371630

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

4790 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);(6,7)(9,10,12,11)(13,14)(15,17)(16,19)(18,20);(5,6,8,7)(9,11,12,10);(5,7,8,6)(14,17)(15,20)(18,19)

maximal subgroup of	C₂²×#22870, C₂²×#21507, C₂²×#23039, …
maximal normal subgroup of	C₂²×#22870, C₂²×#21507, C₂²×#23039, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278826);