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C₂×#39450 #7636675

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

Aliases

Subgroups

8650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543871);