Finite Group Databasebeta

?

← Prev (#494883) Next (#494885) →

C₂×#13141 #494884

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

Aliases

Subgroups

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(4,5)(7,8)(9,19)(10,22,24,30)(11,25)(12,14)(13,18)(15,20,33,38)(16,27)(17,21)(23,35,26,36)(28,34,37,32)(29,31);(3,4,6,5)(7,9,11,12,13,21,27,29)(8,14,16,19,18,31,25,17)(10,20,26,28,24,38,23,37)(15,30,34,36,33,22,32,35);(3,5,6,4)(7,10,13,24)(8,15,18,33)(9,20,21,38)(11,26,27,23)(12,28,29,37)(14,30,31,22)(16,34,25,32)(17,35,19,36)

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, 402080);