Finite Group Databasebeta

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C₂×#5677 #86074

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1620 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)(12,17)(14,16);(1,2)(7,9)(10,12,13,17)(11,14,15,16);(10,11,13,15)(12,16,17,14);(4,5)(7,9);(1,2)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18650);