Finite Group Databasebeta

?

← Prev (#7666157) Next (#7666159) →

C₂×#59453 #7666158

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

Aliases

Subgroups

6314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573354);