Finite Group Databasebeta

?

← Prev (#10577955) Next (#10577957) →

C₂×#61783 #10577956

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

Aliases

Subgroups

6558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 10485152);