Finite Group Databasebeta

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C₂₉×#3532 #16817246

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1336 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)(35,40)(39,42)(41,44)(43,45);(30,32)(31,35)(33,40)(34,39)(36,43)(37,38)(41,45)(42,44);(31,36)(32,39)(37,44)(40,45);(31,36)(32,40)(35,42)(37,44)(38,43)(39,45);(31,37)(35,38)(36,44)(42,43)

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, 2264);