Finite Group Databasebeta

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C₂×#5689 #86094

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(6,8,9,13)(7,10,11,12)(14,16)(15,19)(17,20)(18,21);(6,7,9,11)(8,12,13,10)(15,18)(16,20);(14,15,17,18)(16,19,20,21);(4,5)(16,20)(19,21);(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, 18670);