Finite Group Databasebeta

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C₂×#5196 #83908

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16484);