Finite Group Databasebeta

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C₂×#5642 #85966

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1124 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)(7,10,11,13)(14,16,17,21)(15,19,18,20);(6,7,9,11)(8,13,12,10);(14,15)(16,20)(17,18)(19,21);(4,5)(8,12)(10,13)(15,18)(19,20);(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, 18542);