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C₂²×#36455 #72301142

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

Aliases

Subgroups

131865 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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