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C₂×#18537 #6348083

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

Aliases

Subgroups

3398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255279);