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C₂×#35721 #7629323

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

Aliases

Subgroups

6304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536519);