C₂×#8136 #181810

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1178 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 512

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89006);