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C₂²×#7630940 #72324160

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

Aliases

Subgroups

2080696 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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