Finite Group Databasebeta

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C₁₉×#1711 #14559568

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,32)(24,26)(25,30)(27,29)(31,34)(33,35)(36,37)(38,44)(39,41)(40,48)(42,46)(43,47)(45,50)(49,51);(20,22,29,35,24,31,23,30)(21,25,32,34,26,33,27,28)(37,41)(42,49)(43,48)(44,50);(21,26)(25,33)(27,32)(28,34)(36,38,40,46,39,45,47,51)(37,42,43,44,41,49,48,50)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 443);