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C₂₉×#2070 #16815784

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 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)(30,31,34,48,35,39,50,38)(32,40,42,36,43,56,60,52)(33,44,46,53,47,37,49,54)(41,57,58,51,45,55,59,61);(30,32,34,42,35,43,50,60)(31,36,38,40,39,52,48,56)(33,45,46,59,47,41,49,58)(37,51,53,57,44,61,54,55);(30,33,35,47)(31,37,39,44)(32,41,43,45)(34,49,50,46)(36,51,52,61)(38,54,48,53)(40,55,56,57)(42,59,60,58)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 802);