Finite Group Databasebeta

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C₂×#5517 #85721

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1168 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)(7,10)(9,12)(11,13)(14,16,17,21)(15,18,19,20);(6,7,9,11)(8,10,12,13);(8,12)(10,13);(4,5)(14,15,17,19)(16,20,21,18);(1,2)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18297);