C₂×#11155 #357877

order	512
nilpotency class	3
isoclinism	isoclinic class of #9103
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3250 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(7,8,11,16,12,13,10,15)(9,17,18,21,19,22,20,14);(3,4)(5,6)(8,13)(10,11)(17,22)(18,20);(4,6)(7,9)(8,14,13,21)(10,18)(11,20)(12,19)(15,17,16,22)

maximal subgroup of	C₂×#417558, C₂×#364929, C₂×#394514
maximal normal subgroup of	C₂×#417558, C₂×#364929, C₂×#394514

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265073);