Finite Group Databasebeta

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C₂₉×#3063 #16816777

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

472 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)(34,35,39,43)(36,44,46,47)(37,41,40,49)(38,45,48,42);(34,36,38,41,39,46,48,49)(35,40,42,44,43,37,45,47);(31,33)(34,37)(35,41)(36,45)(38,47)(39,40)(42,46)(43,49)(44,48);(36,46)(37,40)(41,49)(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, 1795);