Finite Group Databasebeta

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C₂×#5721 #86202

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(6,9,10,8)(7,12,13,11)(14,17,18,21)(15,19,16,20);(8,9)(11,12)(14,16,18,15)(17,19,21,20);(6,8,10,9)(7,11,13,12);(4,5)(6,7,10,13)(8,11,9,12)(14,15,18,16)(17,20,21,19);(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, 18778);