Finite Group Databasebeta

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C₂₉×#2333 #16816047

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

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, 1065);