Finite Group Databasebeta

?

← Prev (#7706372) Next (#7706374) →

C₂×#50830 #7706373

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

Aliases

Subgroups

6364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613569);