Finite Group Databasebeta

?

← Prev (#72324195) Next (#72324197) →

C₂²×#7633039 #72324196

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

Aliases

Subgroups

5683552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

488 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((6,8)(9,10,12,11)(13,14)(15,19)(16,18)(17,20), (13,14,17,20)(15,18,16,19), (10,11)(13,14)(15,18)(16,19)(17,20), (10,11)(13,15,17,16)(14,18,20,19), (3,4), (10,11), (1,2)(3,4), (5,6,7,8)(9,11,12,10)(13,16,17,15)(14,19,20,18));