Finite Group Databasebeta

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C₁₉×#2836 #14560693

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

358 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)(21,24)(25,27)(28,29,32,31)(30,33,34,35)(36,37)(38,42)(39,43)(40,41);(22,26)(25,27)(29,31)(30,34)(37,41)(39,42);(20,21,23,24)(22,25,26,27)(28,30)(29,33)(31,35)(32,34)(36,38)(37,42)(39,41)(40,43);(20,22)(21,25)(23,26)(24,27)(28,31,32,29)(30,33,34,35)(36,39,40,42)(37,43,41,38)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1568);