C₂×#7032 #95106

order	512
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

2354 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 2302);