C₂×#9684 #204574

order	512
nilpotency class	3
isoclinism	isoclinic class of #7694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2226 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)(9,13)(10,14)(11,12)(15,16)(17,19,21,22)(18,20);(7,9,13,8,11,14,10,12)(15,17,18,21)(16,19)(20,22);(3,4,5,6)(8,12)(9,14)(16,20)(17,21)

maximal subgroup of	C₂×#261360, C₂×#261403, C₂×#261347, …
maximal normal subgroup of	C₂×#261360, C₂×#261403, C₂×#261347, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111770);