Finite Group Databasebeta

?

← Prev (#7706272) Next (#7706274) →

C₂×#50746 #7706273

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

Aliases

Subgroups

8194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613469);