Finite Group Databasebeta

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C₂×#5685 #86086

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18662);