Finite Group Databasebeta

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C₂₉×#3289 #16817003

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(30,31,36,42)(32,43,47,58)(33,39,49,57)(34,41,35,40)(37,50,54,46)(38,51,55,48)(44,52,61,53)(45,59,60,56);(30,32,36,47)(31,37,42,54)(33,44,49,61)(34,50,35,46)(38,52,55,53)(39,56,57,59)(40,58,41,43)(45,51,60,48);(30,33)(31,38)(32,44)(34,48)(35,51)(36,49)(37,52)(39,40)(41,57)(42,55)(43,59)(45,50)(46,60)(47,61)(53,54)(56,58);(30,33)(31,39)(32,45)(34,51)(35,48)(36,49)(37,53)(38,40)(41,55)(42,57)(43,59)(44,50)(46,61)(47,60)(52,54)(56,58)

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, 2021);