Finite Group Databasebeta

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C₂₉×#2658 #16816372

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

612 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 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)(39,43)(40,46)(45,51)(48,49);(34,35,36,37)(38,39)(40,47)(41,45)(42,43)(44,46)(48,53)(49,52)(50,51);(30,31)(32,33)(34,35)(36,37)(38,40)(39,44)(41,49)(42,46)(43,47)(45,53)(48,50)(51,52);(38,41,42,50)(39,45,43,51)(40,48,46,49)(44,52,47,53)

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, 1390);