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C₂×#35865 #7629231

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

Aliases

Subgroups

6878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536427);