C₂×#10855 #353694

order	512
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2334 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);(4,6)(7,8)(9,12,15,19)(10,17)(11,13)(14,18)(16,22,21,20);(7,9,10,16,11,15,18,21)(8,12,14,20,13,19,17,22);(3,4,5,6)

maximal subgroup of	C₂×#374595, C₂×#411725, C₂×#364922, …
maximal normal subgroup of	C₂×#374595, C₂×#411725, C₂×#364922, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260890);