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C₂×#51640 #7707627

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

Aliases

Subgroups

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7614823);