Finite Group Databasebeta

?

← Prev (#8102042) Next (#8102044) →

C₂×#54816 #8102043

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

Aliases

Subgroups

8732 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)(13,17)(14,18)(15,16);(3,4,6,8)(5,7,10,9)(11,13,15,18)(12,14,16,17)(19,20,23,24)(21,22,25,26);(12,16)(14,17)(20,24)(21,25);(3,4)(5,7)(6,8)(9,10)(11,14)(12,13)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,14)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009239);