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C₂×#40783 #7638745

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

Aliases

Subgroups

8354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(11,12,15,13)(14,16,18,17)(19,20,23,24)(21,25,26,22);(3,4)(5,9)(6,7)(8,10)(11,12,15,13)(14,17,18,16)(20,24)(22,25);(4,7)(8,9)(12,13)(16,17)(19,21,23,26)(20,25,24,22);(3,4)(5,8)(6,7)(9,10)(11,13,15,12)(14,17,18,16)(19,21)(20,22)(23,26)(24,25);(3,5)(4,8)(6,10)(7,9)(11,14)(12,16)(13,17)(15,18)(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, 7545941);