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C₂×#39696 #7637165

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

Aliases

Subgroups

5842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(12,16)(17,18);(4,7)(8,9)(19,20,23,26)(21,25,22,24);(11,12)(13,17)(14,18)(15,16)(19,21,23,22)(20,24,26,25);(3,5)(4,8)(6,10)(7,9)(11,13,15,14)(12,17,16,18);(3,4)(5,8)(6,7)(9,10)(11,14,15,13)(12,18,16,17)(19,22,23,21)(20,25,26,24)

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, 7544361);