Finite Group Databasebeta

?

← Prev (#72324358) Next (#72324360) →

C₂×#7850073 #72324359

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

Aliases

Subgroups

At least 6804 conjugacy classes of subgroups; only the 31933 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

202 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)(9,12,14,13)(15,16,19,18)(17,20,21,22), (3,4)(5,6)(7,8,10,11)(9,12,14,13)(17,21)(20,22), (3,4)(5,6)(7,8,10,11)(9,13,14,12)(16,18)(17,21), (3,4)(5,6)(8,11)(9,14)(15,17,19,21)(16,20,18,22), (1,2), (4,6)(7,8)(9,12)(10,11)(13,14), (3,4)(5,6)(7,9)(8,12)(10,14)(11,13)(15,18,19,16)(17,20,21,22));