C₂²×#1274 #180858

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁵×C₄²

Aliases

2226 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88054);