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C₂₉×#2742 #16816456

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 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)(30,31,34,33)(32,36,37,35)(38,39)(40,44)(41,43)(42,45)(46,47,50,52)(48,49,53,51);(31,33)(35,36)(38,39,41,43)(40,44,45,42)(46,48,50,53)(47,51,52,49);(30,32)(31,35)(33,36)(34,37)(38,39)(40,42)(41,43)(44,45);(30,33,34,31)(32,36,37,35)(38,40,41,45)(39,42,43,44)(46,49,50,51)(47,48,52,53)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1474);