Finite Group Databasebeta

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C₂×#5658 #86010

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(7,11)(10,13)(14,17,18,15)(16,19,20,21);(6,8,9,12)(7,10,11,13)(14,16,18,20)(15,19,17,21);(6,7)(8,10)(9,11)(12,13)(14,15)(16,19)(17,18)(20,21);(4,5)(16,20)(19,21);(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, 18586);