Finite Group Databasebeta

?

← Prev (#72324182) Next (#72324184) →

C₂²×#7685362 #72324183

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

Aliases

Subgroups

At least 7281 conjugacy classes of subgroups; only the 473408 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

452 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((5,6,8,7)(10,11)(13,14,17,18)(15,20,19,16), (9,10,12,11), (6,7)(10,11)(14,18)(16,20), (5,6)(7,8)(9,11,12,10)(14,18)(15,19), (3,4), (6,7)(13,15)(14,16)(17,19)(18,20), (1,2)(3,4), (5,7,8,6)(13,16)(14,19)(15,18)(17,20));