C₂×#8403 #185919

order	512
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4830 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);(3,4)(5,6)(7,8)(9,10,13,14)(11,12)(15,16,18,20,19,22,17,21);(4,6)(7,9)(8,10)(11,13)(12,14)(16,20)(17,18)(21,22);(7,10)(8,9)(11,14)(12,13)

maximal subgroup of	C₂×#208908, C₂×#208860, C₂×#185958, …
maximal normal subgroup of	C₂×#208908, C₂×#208860, C₂×#185958, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 93115);