C₂×#8404 #185920

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

Aliases

3938 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)(9,10,14,12)(11,13)(15,16,18,20,19,22,17,21);(4,6)(7,9)(8,12)(10,13)(11,14)(16,20)(17,18)(21,22);(7,10,11,12)(8,9,13,14)

maximal subgroup of	C₂×#208872, C₂×#208920, C₂×#185958, …
maximal normal subgroup of	C₂×#208872, C₂×#208920, C₂×#185958, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 93116);