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C₂×#44083 #7668259

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

Aliases

Subgroups

6674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575455);