Finite Group Databasebeta

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C₂×#4821 #78982

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

(3,4,5)(6,9,10,17,11,16,19,8)(7,13,14,12,15,18,21,20);(6,8)(7,12)(9,10)(11,17)(13,21)(14,18)(15,20)(16,19);(1,2)(4,5)(6,7)(8,12)(9,18)(10,14)(11,15)(13,16)(17,20)(19,21);(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, 11558);