Finite Group Databasebeta

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C₂×#5596 #85924

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18500);