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C₂₉×#2884 #16816598

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

716 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)(32,40,43,36)(33,37)(34,38)(35,39)(41,54,57,48)(42,55,59,49)(44,50)(45,51)(46,52)(47,53)(56,61,58,60);(30,32)(31,36)(33,41)(34,42)(35,43)(37,48)(38,49)(39,40)(44,56)(45,57)(46,58)(47,59)(50,60)(51,54)(52,61)(53,55);(30,33,35,45)(31,37,39,51)(32,41,43,57)(34,46,47,44)(36,48,40,54)(38,52,53,50)(42,58,59,56)(49,61,55,60);(30,34,35,47)(31,38,39,53)(32,42,43,59)(33,44,45,46)(36,49,40,55)(37,50,51,52)(41,56,57,58)(48,60,54,61)

Conjugacy classes & character table

1189 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1616);