Finite Group Databasebeta

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C₂₉×#3081 #16816795

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

398 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)(30,31,33,35)(32,36,37,34)(38,39)(40,43)(41,44)(42,46)(45,49)(47,51)(48,50)(52,53);(30,32,33,37)(31,34,35,36)(38,40)(39,43)(41,48)(42,47)(44,50)(45,52)(46,51)(49,53);(39,44)(41,49)(43,50)(45,46)(48,53)(51,52);(40,47)(43,51)(48,53)(50,52)

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, 1813);