Finite Group Databasebeta

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C₂×#5124 #83754

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16330);