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C₂×#36162 #7629797

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

Aliases

Subgroups

10728 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)(16,21)(17,22);(7,9)(8,10)(11,13)(12,14)(15,16,20,21)(17,18,22,19);(3,4)(5,6)(8,12)(9,13)(15,17)(16,18)(19,21)(20,22);(7,9)(8,10)(11,13)(12,14)(15,18,20,19)(16,22,21,17);(7,10)(8,13)(9,12)(11,14)(15,19,20,18)(16,17,21,22)

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, 7536993);