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C₂₉×#3237 #16816951

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

322 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)(32,38)(33,36)(34,37)(35,40)(39,44)(41,43)(42,45)(46,47,51,54)(48,55,56,61)(49,53,50,58)(52,59,60,57);(30,32,34,40)(31,35,37,38)(33,41,42,39)(36,44,45,43)(48,56)(52,60)(55,61)(57,59);(30,33,34,42)(31,36,37,45)(32,39,40,41)(35,43,38,44)(46,48)(47,52)(49,57)(50,59)(51,56)(53,61)(54,60)(55,58);(31,37)(35,38)(36,45)(43,44)(46,49,51,50)(47,53,54,58)(48,57,56,59)(52,61,60,55)

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, 1969);