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C₂×#16682 #611345

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

Aliases

Subgroups

5002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 518541);