Finite Group Databasebeta

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C₂₉×#2931 #16816645

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

500 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)(30,31)(32,33)(34,35,39,42,38,41,47,49)(36,43,45,46,44,40,48,37);(31,33)(34,36)(35,40)(37,42)(38,44)(39,45)(41,43)(46,49)(47,48);(34,37,39,43,38,46,47,40)(35,36,42,45,41,44,49,48);(35,41)(36,44)(42,49)(45,48)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1663);