Finite Group Databasebeta

?

← Prev (#7639420) Next (#7639422) →

C₂×#41365 #7639421

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

Aliases

Subgroups

5976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546617);