Finite Group Databasebeta

?

← Prev (#7636493) Next (#7636495) →

C₂×#39021 #7636494

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

Aliases

Subgroups

6004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543690);