Finite Group Databasebeta

?

← Prev (#10575700) Next (#10575702) →

C₂×#60861 #10575701

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

Aliases

Subgroups

6562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 10482897);