Finite Group Databasebeta

?

← Prev (#6344635) Next (#6344637) →

C₂×#17927 #6344636

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

Aliases

Subgroups

1764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251832);