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C₂×#34993 #7628176

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

Aliases

Subgroups

10666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7535372);