Finite Group Databasebeta

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C₁₉×#2767 #14560624

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 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)(20,21,24,23)(22,26,27,25)(30,33)(31,35)(37,40)(38,42);(21,23)(22,27)(28,29,32,34)(30,31,33,35)(36,37,39,40)(38,43,42,41);(20,22,24,27)(21,25,23,26)(28,30,32,33)(29,31,34,35);(20,23,24,21)(22,26,27,25)(28,31)(29,33)(30,34)(32,35)(36,38,39,42)(37,41,40,43)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1499);