C₂×#10897 #353921

order	512
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2078 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261117);