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C₂₉×#3273 #16816987

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

520 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)(34,35,38,41)(36,42,43,49)(37,46,47,40)(39,44,48,45);(34,36)(35,39)(37,44)(38,43)(40,49)(41,48)(42,46)(45,47);(31,33)(36,43)(39,48)(42,49)(44,45);(36,44)(37,47)(39,49)(40,46)(42,48)(43,45)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2005);