C₂×#10769 #353347

order	512
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

4850 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);(3,4)(5,6)(7,8,10,14,11,13,18,21)(9,12,16,20,15,19,17,22);(7,9)(8,12,13,19)(10,17)(11,15)(14,22,21,20)(16,18);(4,6)(8,13)(10,18)(12,19)(16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260543);