Finite Group Databasebeta

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C₂₉×#3511 #16817225

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1104 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)(31,33)(35,36)(40,44)(42,45);(30,31,34,33)(32,36,37,35)(38,39,41,43)(40,42,44,45);(30,31,34,33)(32,35,37,36)(38,40,41,44)(39,42,43,45);(30,32,34,37)(31,35,33,36);(30,33,34,31)(32,36,37,35)

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, 2243);