Finite Group Databasebeta

?

← Prev (#7628724) Next (#7628726) →

C₂×#35370 #7628725

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

Aliases

Subgroups

7798 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)(19,20,22,24)(21,25,26,23);(3,4)(5,9)(6,7)(8,10)(11,13,15,17)(12,14,16,18)(19,20)(21,23)(22,24)(25,26);(4,7)(8,9)(12,16)(13,17)(19,21,22,26)(20,23,24,25);(3,4)(5,8)(6,7)(9,10)(11,12)(13,14)(15,16)(17,18);(3,5)(4,8)(6,10)(7,9)(11,14)(12,13)(15,18)(16,17)

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, 7535921);