Finite Group Databasebeta

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C₂₉×#3043 #16816757

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

490 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)(36,42)(37,44)(39,46)(41,48)(43,45)(47,49);(30,31,32,33)(34,35)(36,39)(37,41)(38,40)(42,46)(43,47)(44,48)(45,49);(34,36,38,43)(35,39,40,47)(37,45,44,42)(41,49,48,46);(35,40)(39,47)(41,48)(46,49)

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, 1775);