Finite Group Databasebeta

?

← Prev (#483011) Next (#483013) →

C₂×#11913 #483012

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

Aliases

Subgroups

761 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 390208);