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C₂₉×#3214 #16816928

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 45 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)(32,36)(33,35)(34,37)(39,42)(40,43)(44,45);(30,32,33,37)(31,34,35,36)(38,39,41,42)(40,43,44,45);(32,37)(34,36)(38,40)(39,43)(41,44)(42,45);(31,35)(34,36)(38,39,41,42)(40,43,44,45)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1946);