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C₂×#9915 #234455

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

Aliases

Subgroups

3382 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)(9,13)(10,12)(11,14)(15,16)(17,19)(18,20)(21,22);(8,12)(9,10)(13,14)(19,22);(4,6)(7,9,11,10)(8,13,14,12)(15,17)(16,19)(18,21)(20,22)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 141651);