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C₂²×#612459 #72268596

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

Aliases

Subgroups

3409892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

464 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)(10,12)(13,14)(15,16)(17,18,20,19), (3,4), (14,16)(18,19), (10,12), (1,2)(3,4), (14,16), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19,20,18));