Finite Group Databasebeta

?

← Prev (#7666401) Next (#7666403) →

C₂×#59212 #7666402

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

Aliases

Subgroups

6546 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)(11,12,14,16)(13,17,18,15)(20,23)(21,25);(4,7)(8,9)(11,12)(13,15)(14,16)(17,18)(20,23)(24,26);(19,20,22,23)(21,24,25,26);(3,4)(5,8)(6,7)(9,10)(19,21)(20,24)(22,25)(23,26);(3,5,6,10)(4,8,7,9)(11,13,14,18)(12,15,16,17)

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, 7573598);