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C₂²×#35347 #72267596

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

Aliases

Subgroups

330469 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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