C₂²×#1275 #180875

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
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)(15,22,24,28)(16,20)(17,26)(18,21)(19,23,27,25);(13,15,17,25,18,24,16,23)(14,19,20,22,21,27,26,28)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88071);