Finite Group Databasebeta

?

← Prev (#7702093) Next (#7702095) →

C₂×#45464 #7702094

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

Aliases

Subgroups

6644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609290);