Finite Group Databasebeta

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C₂×#5710 #86106

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

(1,2)(3,4,5)(6,8)(7,11)(9,12)(10,13)(14,17,18,19)(15,16,20,21);(6,7,9,10)(8,11,12,13)(14,16)(15,19)(17,20)(18,21);(8,12)(11,13)(14,15,18,20)(16,17,21,19);(4,5)(7,10)(11,13)(16,21)(17,19);(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, 18682);