C₂×#9118 #196368

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

Aliases

1912 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)(8,12)(9,10)(13,14)(16,19,20,21);(7,8,9,14,11,13,10,12)(15,16,17,21,18,20,22,19);(4,6)(7,9,11,10)(8,12,13,14)

maximal subgroup of	C₂×#196416, C₂×#246143, C₂×#246103, …
maximal normal subgroup of	C₂×#196416, C₂×#246143, C₂×#246103, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 103564);