Finite Group Databasebeta

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C₂₉×#3007 #16816721

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

754 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)(34,35,39,43)(36,44,46,49)(37,42,38,41)(40,47,48,45);(34,36)(35,40)(37,45)(38,47)(39,46)(41,44)(42,49)(43,48);(31,33);(34,37,39,38)(35,41,43,42)(36,45,46,47)(40,44,48,49)

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, 1739);