C₂×#13759 #513343

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁶×C₄³

Aliases

5594 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#514490, C₂×#514500, C₂×#514721, …
maximal normal subgroup of	C₂×#514490, C₂×#514500, C₂×#514721, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420539);