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C₂×#40639 #7638678

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

Aliases

Subgroups

6828 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545874);