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C₂₉×#1558 #16815272

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(30,31,32,35,33,34,36,37)(38,39)(40,46)(41,49)(42,44)(43,47)(45,51)(48,53)(50,52);(31,34)(32,36)(38,40,42,48)(39,43,44,52)(41,50,51,47)(45,53,49,46);(39,44)(43,52)(45,49)(46,53)

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, 290);