Finite Group Databasebeta

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C₃×#65980 #11755657

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

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, 9852);