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C₂×#62137 #10579385

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

Aliases

Subgroups

7418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10486581);