Finite Group Databasebeta

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C₂₉×#2496 #16816210

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

468 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)(31,32)(34,35,37,39)(36,40,41,38)(44,48)(46,49);(30,31,33,32)(34,35)(36,38)(37,39)(40,41)(42,43,45,47)(44,49,48,46);(34,35)(36,38)(37,39)(40,41)(42,44)(43,46)(45,48)(47,49);(30,32,33,31)(34,36,37,41)(35,38,39,40)

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, 1228);