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C₂²×#58991 #72236655

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

Aliases

Subgroups

248685 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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