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C₂×#13423 #499130

• p-group
• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

1516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406326);