Finite Group Databasebeta

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C₂₉×#2628 #16816342

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

488 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)(34,35)(36,39)(37,38)(40,41)(42,43,46,49)(44,47,48,45);(31,33)(35,38)(39,40)(42,44)(43,47)(45,49)(46,48);(30,31)(32,33)(34,35)(36,40)(37,38)(39,41)(42,45,46,47)(43,48,49,44);(34,36,37,41)(35,39,38,40)

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, 1360);