Finite Group Databasebeta

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C₂₉×#2592 #16816306

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

520 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)(34,35,37,39)(36,40,41,38)(43,45)(44,48);(34,35)(36,38)(37,39)(40,41)(42,43,46,45)(44,49,48,47);(30,31)(32,33)(34,35)(36,38)(37,39)(40,41)(42,44,46,48)(43,47,45,49);(34,36,37,41)(35,38,39,40)(42,45,46,43)(44,49,48,47)

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, 1324);