Finite Group Databasebeta

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C₂×#5236 #84078

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(3,4,5)(6,8)(7,11)(9,17)(10,16)(12,15)(13,21)(14,20)(18,19);(1,2)(8,16)(11,20)(15,21)(17,18);(4,5)(6,7,9,12,10,14,19,13)(8,15,17,20,16,21,18,11);(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, 16654);