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C₂×#36161 #7629796

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

Aliases

Subgroups

10582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536992);