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C₂×#14335 #515241

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

Aliases

Subgroups

31666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422437);