Finite Group Databasebeta

?

← Prev (#495200) Next (#495202) →

C₂×#13234 #495201

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

Aliases

Subgroups

1256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402397);