Finite Group Databasebeta

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C₂₉×#2695 #16816409

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

504 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)(34,35)(36,38)(37,39)(40,41)(42,43)(44,49)(45,48)(46,47);(31,33)(35,36)(37,41)(42,44,47,45)(43,48,46,49);(30,31)(32,33)(34,36,38,35)(37,40,41,39)(42,45,47,44)(43,48,46,49);(34,37,38,41)(35,39,36,40)(42,46,47,43)(44,48,45,49)

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, 1427);