Finite Group Databasebeta

?

← Prev (#72295996) Next (#72295998) →

C₂³×#35390 #72295997

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

Aliases

Subgroups

4685208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 22 points:

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

Conjugacy classes & character table

512 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((8,10)(11,12)(13,14)(15,16)(17,21)(18,19)(20,22), (8,10)(12,13)(15,16)(17,20)(18,19)(21,22), (16,19)(20,21), (7,8,9,10)(11,13,14,12)(15,16)(17,20)(18,19)(21,22), (3,4), (15,17)(16,20)(18,22)(19,21), (5,6), (1,2)(3,4)(5,6));