Finite Group Databasebeta

?

← Prev (#6359640) Next (#6359642) →

C₂×#20284 #6359641

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

Aliases

Subgroups

1643 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,9)(5,7)(10,12)(11,17)(13,16)(14,18)(19,20)(21,28)(22,26)(23,31)(24,27)(25,30)(29,34)(32,33);(3,4,8,12)(5,9,7,10)(6,14,15,17)(11,16,18,13)(21,29)(25,33)(28,34)(30,32);(3,5,8,7)(4,10,12,9)(6,13,15,16)(11,14,18,17)(19,21,24,29)(20,25,27,33)(22,30,23,32)(26,34,31,28);(3,6,8,15)(4,11,12,18)(5,13,7,16)(9,17,10,14)(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, 6266837);