C₂²×#1281 #181050

order	512
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1970 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2);(3,4);(5,6,7,9,8,10,11,12)(13,14)(15,21,22,18)(16,20)(17,19)(23,27,28,25)(24,26);(13,15,16,23,17,22,24,28)(14,18,20,25,19,21,26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88246);