Finite Group Databasebeta

?

← Prev (#498834) Next (#498836) →

C₂×#13323 #498835

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

Aliases

Subgroups

1540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406031);