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C₂₉×#3284 #16816998

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

494 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)(34,35,40,37)(36,44,47,49)(38,43,39,42)(41,48,45,46);(34,36,40,47)(35,41,37,45)(38,46,39,48)(42,44,43,49);(31,33)(34,37,40,35)(36,45,47,41)(38,43,39,42)(44,46,49,48);(34,38)(35,42)(37,43)(39,40)(44,49)(46,48)

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, 2016);