Finite Group Databasebeta

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C₂×#5768 #87183

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1484 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)(7,12)(9,18)(10,14)(11,20)(13,21)(15,17)(16,19);(1,2)(6,7)(8,15)(9,17)(10,11)(12,16)(13,19)(14,21)(18,20);(7,11)(8,14)(13,17)(16,18);(4,5)(8,14)(12,20)(15,21)(16,18);(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, 19759);