Finite Group Databasebeta

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C₂₉×#3054 #16816768

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

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, 1786);