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C₂×#17745 #6344035

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

Aliases

Subgroups

4440 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)(11,12,14,16,15,17,13,18);(3,4)(5,8)(6,10)(7,9)(12,16)(13,14)(17,18);(3,5,7,6)(4,8,9,10)(12,17)(16,18);(3,5,7,6)(4,8,9,10)

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, 6251231);