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C₂²×#9463 #72291670

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

Aliases

Subgroups

29909 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

148 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((1,2)(3,4)(15,20)(17,18), (5,6,7,10)(8,11,12,9)(13,14)(15,17)(16,19)(18,20), (5,6)(7,9)(8,11)(10,12)(14,17,19,18), (1,2), (3,4));