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C₂×#5574 #85792

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 17 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18368);