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C₂×#39135 #7637080

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

Aliases

Subgroups

10204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544276);