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C₂₉×#3056 #16816770

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

496 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)(37,45,46,40)(39,47,48,44);(34,36,37,44,38,43,46,47)(35,39,40,42,41,48,45,49);(31,33);(36,43)(39,48)(42,49)(44,47)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1788);