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C₂×#34299 #7625606

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

Aliases

Subgroups

8138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532802);