Finite Group Databasebeta

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C₂×#5197 #83909

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

464 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)(7,13)(8,14)(10,19)(11,21)(12,20)(15,18)(16,17);(1,2)(6,8)(7,9)(10,17)(11,13)(12,18)(14,19)(15,21)(16,20);(4,5)(6,7,10,14,12,16,11,15)(8,9,17,19,18,20,13,21);(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, 16485);