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C₂×#17592 #6343367

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

Aliases

Subgroups

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250563);