Finite Group Databasebeta

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C₃×#66150 #11755827

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2,3)(4,5,7,8,6)(10,12)(13,16,17,24)(14,20,19,27)(15,21,22,23)(18,26,25,28);(14,19)(18,25)(20,27)(26,28);(13,15,17,22)(14,18,19,25)(16,23,24,21)(20,28,27,26);(5,6)(7,8)(9,10)(11,12)(13,14)(15,18)(16,20)(17,19)(21,26)(22,25)(23,28)(24,27)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10022);