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C₂₉×#2844 #16816558

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(30,31,33,35)(32,34,36,37)(38,39,42,41)(40,43,44,45);(32,36)(34,37)(39,41)(43,45)(46,47,49,51)(48,52,53,50);(30,31)(32,34)(33,35)(36,37)(38,40)(39,43)(41,45)(42,44)(46,48,49,53)(47,50,51,52);(30,32)(31,34)(33,36)(35,37)(38,41,42,39)(40,43,44,45)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1576);