Finite Group Databasebeta

?

← Prev (#72332237) Next (#72332239) →

C₂×#8077889 #72332238

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

Aliases

Subgroups

At least 10428 conjugacy classes of subgroups; only the 31829 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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