Finite Group Databasebeta

?

← Prev (#7629991) Next (#7629993) →

C₂×#36339 #7629992

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

Aliases

Subgroups

8012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537188);