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C₂²×#35565 #72320610

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

Aliases

Subgroups

170733 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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