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C₂×#13349 #498921

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

Aliases

Subgroups

2380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406117);