Finite Group Databasebeta

?

← Prev (#7634709) Next (#7634711) →

C₂×#37290 #7634710

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

Aliases

Subgroups

6610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541906);