Finite Group Databasebeta

?

← Prev (#6342995) Next (#6342997) →

C₂×#17491 #6342996

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

Aliases

Subgroups

3138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250192);