Finite Group Databasebeta

?

← Prev (#72299013) Next (#72299015) →

C₂×#7903989 #72299014

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

Aliases

Subgroups

At least 10982 conjugacy classes of subgroups; only the 31893 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

190 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)(9,13)(10,14)(11,12)(16,19)(20,22), (4,6)(9,14)(10,13)(16,19)(17,21), (8,12)(10,13)(16,19)(20,22), (3,4,5,6)(7,9,11,14)(8,10,12,13)(15,16,18,19)(17,22,21,20), (7,9)(8,10)(11,14)(12,13), (3,4)(5,6)(7,10)(8,9)(11,13)(12,14)(15,17)(16,20)(18,21)(19,22), (1,2));