Finite Group Databasebeta

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C₂×#5546 #85749

• 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:

(3,4,5)(6,7,8,9)(11,15)(14,17);(1,2)(10,12)(11,14)(13,16)(15,17);(10,11,13,15)(12,17,16,14);(4,5)(12,16)(14,17);(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, 18325);