C₂×#7862 #180879

order	512
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1762 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88075);