Finite Group Databasebeta

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C₂₉×#3490 #16817204

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1328 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)(32,38)(33,37)(34,36)(35,39)(40,44)(41,43)(42,45);(30,32,34,40)(31,35,36,42)(33,39,41,45)(37,38,43,44);(31,36)(35,42)(37,43)(38,44);(32,39)(35,38)(40,45)(42,44);(31,37)(35,38)(36,43)(42,44)

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, 2222);