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C₂²×#35001 #72278506

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

Aliases

Subgroups

179741 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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