Finite Group Databasebeta

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C₃×#66046 #11755723

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3)(4,5,7,8,6)(9,11,12,15)(10,14,13,16)(18,24)(19,26)(20,28)(29,31);(10,13)(14,16)(17,20)(18,23)(19,25)(21,28)(22,29)(24,27)(26,32)(30,31);(9,10)(11,14)(12,13)(15,16)(17,19,21,26)(18,22,24,30)(20,25,28,32)(23,29,27,31);(5,6)(7,8)(11,15)(14,16)(17,18)(19,22)(20,27)(21,24)(23,28)(25,31)(26,30)(29,32)

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9918);