Finite Group Databasebeta

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C₂₉×#2664 #16816378

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

434 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)(35,38)(39,41)(42,43,46,45)(44,48,49,47);(30,31,32,33)(42,44)(43,47)(45,48)(46,49);(30,31)(32,33)(34,35)(36,39)(37,38)(40,41)(42,45,46,43)(44,48,49,47);(34,36,37,40)(35,39,38,41)(42,44)(43,48)(45,47)(46,49)

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, 1396);