Finite Group Databasebeta

?

← Prev (#72262597) Next (#72262599) →

C₂×#72233689 #72262598

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

Aliases

Subgroups

4377438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

362 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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