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C₂²×#3483 #10585939

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

Aliases

Subgroups

40334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493135);