Finite Group Databasebeta

?

← Prev (#72331230) Next (#72331232) →

C₂×#72240166 #72331231

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

Aliases

Subgroups

At least 7376 conjugacy classes of subgroups; only the 48360 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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((7,8)(9,10)(12,14)(15,16,18,20)(17,19,21,22), (11,12)(13,14)(17,21)(19,22), (15,17)(16,19)(18,21)(20,22), (1,2), (4,6)(8,10)(11,12)(13,14), (15,16)(17,19)(18,20)(21,22), (3,4)(5,6)(7,8)(9,10)(15,17)(16,19)(18,21)(20,22));