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C₂₉×#3223 #16816937

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 69 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)(32,36)(33,35)(34,37)(38,39,43,47)(40,44,49,58)(41,51,53,61)(42,54,56,46)(45,55,60,52)(48,62,63,69)(50,66,65,59)(57,67,68,64);(30,32,33,37)(31,34,35,36)(38,40)(39,44)(41,48)(42,50)(43,49)(45,57)(46,59)(47,58)(51,62)(52,64)(53,63)(54,66)(55,67)(56,65)(60,68)(61,69);(32,37)(34,36)(38,41,43,53)(39,45,47,60)(40,48,49,63)(42,55,56,52)(44,57,58,68)(46,61,54,51)(50,67,65,64)(59,69,66,62);(31,35)(34,36)(40,49)(44,58)(48,63)(50,65)(57,68)(59,66)(62,69)(64,67)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1955);