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C₂₉×#2955 #16816669

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 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)(30,31,35,40,36,39,34,48)(32,41,43,37,44,52,49,51)(33,38,46,54,47,53,45,58)(42,55,56,50,57,61,59,60);(30,32)(31,37)(33,42)(34,49)(35,43)(36,44)(38,50)(39,51)(40,52)(41,48)(45,59)(46,56)(47,57)(53,60)(54,61)(55,58);(30,33,35,46,36,47,34,45)(31,38,40,54,39,53,48,58)(32,42,43,56,44,57,49,59)(37,50,52,61,51,60,41,55);(31,39)(37,51)(38,53)(40,48)(41,52)(50,60)(54,58)(55,61)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1687);