Finite Group Databasebeta

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C₂₉×#3057 #16816771

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

492 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)(37,44)(40,45)(41,46)(43,48)(47,49);(34,35,37,39,38,41,44,46)(36,40,43,45,42,47,48,49);(31,33)(34,36)(35,40)(37,43)(38,42)(39,45)(41,47)(44,48)(46,49);(36,42)(40,47)(43,48)(45,49)

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, 1789);