Finite Group Databasebeta

?

← Prev (#8102588) Next (#8102590) →

C₂×#53393 #8102589

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

Aliases

Subgroups

7294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009785);