Finite Group Databasebeta

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C₂₉×#2477 #16816191

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

540 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)(34,35,37,39)(36,40,41,38)(42,43)(44,45)(46,48)(47,49);(31,33)(34,36,37,41)(35,38,39,40)(42,44,46,49)(43,45,48,47);(30,31)(32,33)(34,36)(35,38)(37,41)(39,40)(42,44)(43,47)(45,48)(46,49);(34,35)(36,38)(37,39)(40,41)(42,45,46,47)(43,44,48,49)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1209);