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C₂²×#33688 #72226769

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

Aliases

Subgroups

12549 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

136 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((5,6)(7,10)(8,18)(9,12)(11,16)(13,17)(14,19)(15,20), (7,14)(10,19)(13,20)(15,17), (6,10,12,19)(7,15)(8,16)(11,13,18,20)(14,17), (6,11,12,18)(7,14)(10,13,19,20)(15,17), (1,2)(6,12)(10,19)(11,18)(13,20), (3,4)(6,12)(10,19)(11,18)(13,20));