Finite Group Databasebeta

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C₂₉×#3558 #16817272

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 45 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)(32,34)(33,36)(35,37)(39,42)(40,44);(31,32)(35,36)(39,42)(43,45);(30,31,34,32)(33,35,37,36)(38,39)(40,43)(41,42)(44,45);(30,32,34,31)(33,36,37,35)(38,40,41,44)(39,43,42,45);(30,33)(31,35)(32,36)(34,37)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2290);