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C₂×#59837 #7666733

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

Aliases

Subgroups

8618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573929);