Finite Group Databasebeta

?

← Prev (#72267488) Next (#72267490) →

C₂×#7670250 #72267489

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

Aliases

Subgroups

104761 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((7,8,12,14)(9,11,13,10)(15,16,19,22)(17,21,18,20), (4,6)(7,9,12,13)(8,10,14,11)(15,17,19,18)(16,20,22,21), (4,6)(7,10,12,11)(8,9,14,13)(15,16,19,22)(17,20,18,21), (15,16)(17,21)(18,20)(19,22), (1,2), (7,9)(8,10)(11,14)(12,13)(15,16)(17,21)(18,20)(19,22), (3,4)(5,6)(7,11,12,10)(8,13,14,9)(15,18,19,17)(16,21,22,20));