Finite Group Databasebeta

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C₂×#5592 #85910

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18486);