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C₂₉×#3282 #16816996

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 49 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)(32,33)(34,35,38,40)(36,42,45,49)(37,46,47,41)(39,43,48,44);(34,36,38,45)(35,39,40,48)(37,43,47,44)(41,49,46,42);(31,33);(35,40)(36,43)(37,47)(39,42)(44,45)(48,49)

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2014);