C₂×#11392 #358791

order	512
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3122 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)(16,19)(17,21)(20,22);(7,8,10,12)(9,13,14,11)(15,16)(17,22)(18,20)(19,21);(7,9,10,14)(8,11,12,13)(17,21)(19,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265987);