Finite Group Databasebeta

?

← Prev (#233564) Next (#233566) →

C₂×#10013 #233565

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

Aliases

Subgroups

1660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 140761);