Finite Group Databasebeta

?

← Prev (#233347) Next (#233349) →

C₂×#10307 #233348

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

Aliases

Subgroups

2164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4)(5,6)(7,8)(9,12)(10,14)(11,13)(16,20)(17,21)(18,22);(4,6)(8,12)(9,11)(13,14)(15,16)(17,19)(18,21)(20,22);(7,8,10,14)(9,12,11,13)(15,17,19,16)(18,20,22,21)

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, 140544);