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C₂²×#10586472 #72299725

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

Aliases

Subgroups

9732072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 9 generators on 20 points:

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

Conjugacy classes & character table

584 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((6,9)(10,12)(13,14)(15,19)(16,17)(18,20), (7,11)(10,12)(14,17)(18,19), (5,6)(7,12)(8,9)(10,11)(15,20)(18,19), (5,6)(7,12)(8,9)(10,11)(13,15)(14,18)(16,20)(17,19), (5,6,8,9)(7,12,11,10)(13,14)(15,19)(16,17)(18,20), (5,6)(7,10)(8,9)(11,12), (5,7)(6,10)(8,11)(9,12)(13,14)(15,19)(16,17)(18,20), (3,4), (1,2)(3,4));