Finite Group Databasebeta

?

← Prev (#60855) Next (#60857) →

C₂×#3242 #60856

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

Aliases

Subgroups

839 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53844);