Finite Group Databasebeta

?

← Prev (#7637180) Next (#7637182) →

C₂×#39687 #7637181

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

Aliases

Subgroups

5798 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)(13,15)(14,17)(16,18)(19,20)(21,23)(22,25)(24,26);(11,13,14,18)(12,15,17,16)(20,21)(24,25);(3,4,6,7)(5,8,9,10)(11,13)(12,16)(14,18)(15,17)(19,21,23,20)(22,25,26,24);(19,22)(20,24)(21,25)(23,26);(3,5,6,9)(4,8,7,10)(11,12)(13,16)(14,17)(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, 7544377);