C₂×#13842 #514007

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

5930 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421203);