Finite Group Databasebeta

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C₂×#5678 #86071

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(6,8,9,12)(7,11,10,13)(15,19)(18,21);(7,10)(11,13)(14,16,17,20)(15,18,19,21);(6,7)(8,11)(9,10)(12,13)(14,15)(16,18)(17,19)(20,21);(4,5)(8,12)(11,13);(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, 18647);