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C₂₉×#2017 #16815731

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 points:

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 749);