Finite Group Databasebeta

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C₂₉×#3288 #16817002

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(31,36)(33,34)(37,44)(38,42)(39,45)(40,43);(30,31)(32,39)(33,42)(34,36)(35,38)(37,40)(41,44)(43,45);(30,31)(32,37)(33,36)(34,42)(35,38)(39,40)(41,45)(43,44);(30,32)(31,37)(33,43)(34,40)(35,41)(36,44)(38,45)(39,42)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2020);