Finite Group Databasebeta

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C₂₉×#3041 #16816755

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

526 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)(31,33)(34,35)(36,39)(37,40)(38,42)(41,45)(43,47)(44,46)(48,49);(30,31,32,33)(34,36)(35,39)(37,44)(38,43)(40,46)(41,48)(42,47)(45,49);(35,40)(37,45)(39,46)(41,42)(44,49)(47,48);(36,43)(39,47)(44,49)(46,48)

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, 1773);