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C₂₉×#3069 #16816783

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

446 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)(30,31,36,41)(32,42,44,53)(33,47,49,55)(34,40,35,39)(37,46,52,45)(38,50,54,48)(43,57,58,51)(56,60,61,59);(30,32,34,45,36,44,35,46)(31,37,39,42,41,52,40,53)(33,43,48,59,49,58,50,60)(38,51,47,56,54,57,55,61);(30,33)(31,38)(32,43)(34,48)(35,50)(36,49)(37,51)(39,47)(40,55)(41,54)(42,56)(44,58)(45,59)(46,60)(52,57)(53,61);(32,44)(37,52)(42,53)(43,58)(45,46)(51,57)(56,61)(59,60)

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, 1801);