Finite Group Databasebeta

?

← Prev (#6359641) Next (#6359643) →

C₂×#20285 #6359642

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

Aliases

Subgroups

1579 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266838);