Finite Group Databasebeta

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C₂₉×#2500 #16816214

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

568 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)(31,33)(34,35)(36,40)(37,38)(39,41)(42,43,45,47)(44,48,49,46);(35,38)(39,40)(42,43)(44,46)(45,47)(48,49);(30,31,32,33)(34,35)(36,39)(37,38)(40,41);(34,36,37,41)(35,39,38,40)(42,44,45,49)(43,46,47,48)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1232);