Finite Group Databasebeta

?

← Prev (#6431844) Next (#6431846) →

C₂×#23474 #6431845

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

Aliases

Subgroups

3898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339041);