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C₂²×#37644 #72236643

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

Aliases

Subgroups

254405 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)(16,17)(18,20);(6,8)(9,10,11,12)(13,14,17,16)(15,19,20,18);(6,8)(9,10)(11,12)(14,16)(15,20);(13,15)(14,18)(16,19)(17,20);(5,6,7,8)(9,10)(11,12)(13,16,17,14)(15,18,20,19)

Conjugacy classes & character table

232 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)(16,17)(18,20), (6,8)(9,10,11,12)(13,14,17,16)(15,19,20,18), (6,8)(9,10)(11,12)(14,16)(15,20), (13,15)(14,18)(16,19)(17,20), (5,6,7,8)(9,10)(11,12)(13,16,17,14)(15,18,20,19));