C₂×#8332 #185006

order	512
nilpotency class	3
isoclinism	isoclinic class of #7606
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3978 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)(9,11)(10,13)(12,14)(16,20,21,22);(8,11)(9,14)(12,13)(15,16)(17,20)(18,22)(19,21);(4,6)(15,17,19,18)(16,20,21,22)

maximal subgroup of	C₂×#246143, C₂×#185043, C₂×#246103, …
maximal normal subgroup of	C₂×#246143, C₂×#185043, C₂×#246103, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 92202);