C₂×#9113 #196357

order	512
nilpotency class	3
isoclinism	isoclinic class of #7654
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3452 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)(8,11)(9,12)(13,14)(15,16)(17,19,21,22)(18,20);(7,8,12,14,10,13,9,11)(15,17,18,21)(16,19)(20,22);(4,6)

maximal subgroup of	C₂×#255122, C₂×#257042, C₂×#246039, …
maximal normal subgroup of	C₂×#255122, C₂×#257042, C₂×#246039, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 103553);