Finite Group Databasebeta

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C₂₉×#2813 #16816527

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

578 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)(35,38)(39,41)(42,43,45,46)(44,47,49,48);(31,33)(35,38)(36,40)(43,46)(47,48);(30,31)(32,33)(34,35)(36,39)(37,38)(40,41)(42,43)(44,48)(45,46)(47,49);(34,36)(35,39)(37,40)(38,41)(42,44)(43,47)(45,49)(46,48)

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, 1545);