Finite Group Databasebeta

?

← Prev (#358605) Next (#358607) →

C₂×#11349 #358606

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265802);