C₂×#10949 #354039

order	512
nilpotency class	3
isoclinism	isoclinic class of #1909
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

3062 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	C₂×#417819, C₂×#422790, C₂×C₄×#1911, …
maximal normal subgroup of	C₂×#417819, C₂×#422790, C₂×C₄×#1911, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261235);