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C₂×#35056 #7628245

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

Aliases

Subgroups

7648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535441);