Finite Group Databasebeta

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C₂₉×#3012 #16816726

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

764 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)(36,41)(37,42)(38,47)(39,43)(40,44)(45,48)(46,49);(34,36)(35,40)(37,44)(38,46)(39,45)(41,47)(42,48)(43,49);(31,33)(34,36)(35,41)(37,46)(38,44)(39,45)(40,47)(42,49)(43,48);(34,37,39,38)(35,42,43,47)(36,44,45,46)(40,48,49,41)

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, 1744);