Finite Group Databasebeta

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C₂₉×#3514 #16817228

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1142 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)(32,37)(33,36)(34,35)(39,42)(43,45);(31,35)(36,37);(30,32,34,33)(31,36,35,37)(38,39)(40,43)(41,42)(44,45);(30,31)(32,36)(33,37)(34,35);(30,33,34,32)(31,37,35,36)(38,40,41,44)(39,43,42,45)

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, 2246);