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C₂₉×#1658 #16815372

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(31,36)(32,39)(33,34)(38,41)(40,42)(43,44)(47,51)(49,56)(52,60)(53,57)(54,58)(59,61);(30,31)(32,37)(33,41)(34,36)(35,38)(39,44)(40,45)(42,43)(46,47,50,53)(48,52,55,61)(49,57,56,51)(54,59,58,60);(30,32,35,40)(31,37,38,45)(33,39,34,42)(36,43,41,44)(46,48,50,55)(47,52,53,61)(49,58,56,54)(51,59,57,60)

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 390);