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C₂₉×#3523 #16817237

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 53 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)(31,34)(35,37)(38,39,43,41)(40,46,48,44)(42,49,50,45)(47,51,53,52);(38,40,43,48)(39,44,41,46)(42,47,50,53)(45,51,49,52);(30,31)(32,35)(33,34)(36,37);(38,41,43,39)(40,44,48,46)(42,49,50,45)(47,51,53,52);(30,32,33,36)(31,35,34,37)(38,42,43,50)(39,45,41,49)(40,47,48,53)(44,51,46,52)

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, 2255);