Finite Group Databasebeta

?

← Prev (#6358411) Next (#6358413) →

C₂×#20017 #6358412

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

Aliases

Subgroups

1686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265608);