Finite Group Databasebeta

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C₂×#5634 #85979

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1296 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)(7,11)(9,12)(10,13)(14,17,18,21)(15,19,16,20);(7,10)(11,13)(14,16,18,15)(17,19,21,20);(6,7)(8,11)(9,10)(12,13)(14,15)(16,18)(17,19)(20,21);(4,5)(8,12)(11,13)(17,21)(19,20);(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, 18555);