Finite Group Databasebeta

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C₂₉×#2726 #16816440

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

416 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)(34,35)(36,38)(37,39)(40,41)(42,43,46,49)(44,47,48,45);(31,33)(35,36)(37,41)(42,44,46,48)(43,47,49,45);(30,31)(32,33)(34,36,38,35)(37,40,41,39)(42,45,46,47)(43,48,49,44);(34,37,38,41)(35,39,36,40)(42,43)(44,47)(45,48)(46,49)

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, 1458);