Finite Group Databasebeta

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C₂×#5964 #87565

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

5956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 21 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 20141);