Finite Group Databasebeta

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C₃×#60398 #10679005

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 35 points:

(1,2,3)(4,5)(6,10)(7,11)(8,13)(9,12)(14,26)(15,22)(16,21)(17,24)(18,23)(19,25)(20,28)(27,34)(29,32)(30,33)(31,35);(4,6)(5,10)(7,14)(8,15)(9,16)(11,20)(12,21)(13,22)(17,27)(18,28)(19,29)(23,26)(24,31)(25,32)(30,35)(33,34);(4,7)(5,11)(6,14)(8,17)(9,18)(10,20)(12,23)(13,24)(15,27)(16,28)(19,30)(21,26)(22,31)(25,33)(29,35)(32,34);(5,12)(10,21)(11,23)(13,25)(20,26)(22,32)(24,33)(31,34);(4,8,9,19)(5,13,12,25)(6,15,16,29)(7,17,18,30)(10,22,21,32)(11,24,23,33)(14,27,28,35)(20,31,26,34)

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 53386);