Finite Group Databasebeta

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C₂₉×#3155 #16816869

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

596 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)(35,39)(37,40)(41,45)(42,46)(44,47)(48,49);(34,35,40,46,38,42,37,39)(36,41,47,49,43,48,44,45);(30,31,32,33)(34,36)(35,41)(37,44)(38,43)(39,45)(40,47)(42,48)(46,49);(36,43)(41,48)(44,47)(45,49)

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, 1887);