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C₃×#7511 #10626118

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 67 points:

(1,2,3)(4,5,6,12,7,14,18,33,8,15,19,34,21,37,42,58,9,16,20,31,22,38,43,54,24,39,44,55,45,60,62,66,10,13,17,32,23,35,40,56,25,36,41,57,46,59,61,67,26,11,27,28,47,29,49,51,48,30,50,52,63,53,64,65);(5,11,13,16)(6,17)(12,31,32,28)(14,29,35,38)(15,30,36,39)(18,40)(19,41)(20,27)(33,54,56,51)(34,55,57,52)(37,53,59,60)(42,61)(43,49)(44,50)(58,66,67,65)(62,64)

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 499);