Finite Group Databasebeta

?

← Prev (#52113) Next (#52115) →

C₂×#2694 #52114

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

Aliases

Subgroups

1361 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45102);