Finite Group Databasebeta

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C₂₉×#3267 #16816981

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

500 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)(37,45)(40,46)(41,42)(43,49)(47,48);(34,35)(36,40)(37,41)(38,42)(39,45)(43,47)(44,48)(46,49);(31,33)(34,36,38,44)(35,40,42,48)(37,43,45,49)(39,46,41,47);(35,41)(37,45)(39,42)(40,47)(43,49)(46,48)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1999);