Finite Group Databasebeta

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C₂₉×#2680 #16816394

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

568 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)(30,31,32,33)(38,39)(40,41)(42,43)(44,45);(35,37)(39,43)(41,45);(30,31)(32,33)(34,35)(36,37)(38,40,42,44)(39,41,43,45);(30,31)(32,33)(38,41)(39,44)(40,43)(42,45)

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, 1412);