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C₂×#15289 #608816

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

Aliases

Subgroups

6158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516012);