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C₂₉×#3127 #16816841

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

358 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)(32,35)(33,34)(36,37)(38,39,42,46)(40,48,50,44)(41,52,53,61)(43,56,55,47)(45,57,60,54)(49,64,65,69)(51,59,67,63)(58,66,62,68);(31,34)(35,37)(38,40)(39,44)(41,49)(42,50)(43,51)(45,58)(46,48)(47,59)(52,69)(53,65)(54,66)(55,67)(56,63)(57,68)(60,62)(61,64);(38,41,42,53)(39,45,46,60)(40,49,50,65)(43,57,55,54)(44,58,48,62)(47,61,56,52)(51,68,67,66)(59,64,63,69);(30,32,33,36)(31,35,34,37)(40,50)(44,48)(49,65)(51,67)(58,62)(59,63)(64,69)(66,68)

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, 1859);