Finite Group Databasebeta

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C₂₉×#3285 #16816999

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2017);