Finite Group Databasebeta

?

← Prev (#72298955) Next (#72298957) →

C₂×#7733277 #72298956

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

Aliases

Subgroups

106341 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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