Finite Group Databasebeta

?

← Prev (#7629974) Next (#7629976) →

C₂×#36322 #7629975

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

Aliases

Subgroups

7114 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)(19,20)(21,26)(22,25)(23,24);(3,5,8,6)(4,9,10,7)(11,12,14,16)(13,15,18,17)(20,24)(21,25);(4,10)(5,6)(11,12)(13,17)(14,16)(15,18)(19,21,23,25)(20,22,24,26);(3,6,8,5)(4,7,10,9)(11,13)(12,15)(14,18)(16,17)(19,22,23,26)(20,25,24,21);(3,7)(4,6)(5,10)(8,9)(11,12)(13,17)(14,16)(15,18)(19,20)(21,22)(23,24)(25,26)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537171);