Finite Group Databasebeta

?

← Prev (#608024) Next (#608026) →

C₂×#14978 #608025

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

Aliases

Subgroups

5126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 515221);