Finite Group Databasebeta

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C₂₉×#3040 #16816754

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

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, 1772);