Finite Group Databasebeta

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C₂₉×#3290 #16817004

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

454 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)(32,41)(33,38)(34,51)(35,40)(36,44)(37,49)(39,52)(42,54)(43,60)(45,56)(46,55)(47,53)(48,58)(50,57)(59,61);(30,32)(31,36)(33,47)(34,45)(35,46)(37,54)(38,59)(39,55)(40,56)(41,51)(42,50)(43,48)(44,52)(49,61)(53,58)(57,60);(30,33)(31,37)(32,42)(34,48)(35,50)(36,53)(38,51)(39,57)(40,58)(41,60)(43,44)(45,61)(46,47)(49,52)(54,56)(55,59);(30,33)(31,38)(32,43)(34,49)(35,50)(36,54)(37,51)(39,58)(40,57)(41,60)(42,44)(45,47)(46,61)(48,52)(53,56)(55,59)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2022);