Finite Group Databasebeta

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C₂₉×#2898 #16816612

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

726 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)(35,39)(37,44)(40,46)(41,45)(43,48)(47,49);(34,35,38,41)(36,40,42,47)(37,45,44,39)(43,49,48,46);(34,36)(35,40)(37,43)(38,42)(39,46)(41,47)(44,48)(45,49);(36,42)(40,47)(43,48)(46,49)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1630);