Finite Group Databasebeta

?

← Prev (#7705411) Next (#7705413) →

C₂×#50097 #7705412

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

Aliases

Subgroups

7224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612608);