Finite Group Databasebeta

?

← Prev (#7704544) Next (#7704546) →

C₂×#49254 #7704545

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

Aliases

Subgroups

6278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611741);