Finite Group Databasebeta

?

← Prev (#7666345) Next (#7666347) →

C₂×#59647 #7666346

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

Aliases

Subgroups

6942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573542);