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C₂₉×#2833 #16816547

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

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, 1565);