Finite Group Databasebeta

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C₁₉×#2508 #14560365

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 43 points:

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

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, 1240);