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C₂₉×#3233 #16816947

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 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)(48,56)(49,55)(50,52)(51,54)(53,58)(57,61)(59,60);(30,32,34,40)(31,35,37,38)(33,41,42,39)(36,44,45,43)(47,52)(48,57)(54,55)(58,59);(30,33,34,42)(31,36,37,45)(32,39,40,41)(35,43,38,44)(46,48,50,57)(47,53,52,60)(49,58,51,59)(54,56,55,61);(31,37)(35,38)(36,45)(43,44)(46,49,50,51)(47,54,52,55)(48,58,57,59)(53,56,60,61)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1965);