Finite Group Databasebeta

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C₁₉×#2802 #14560659

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

360 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)(22,26)(28,29,31,33)(30,34,35,32)(36,37)(38,42)(39,41)(40,43);(21,24)(25,27)(36,37,39,41)(38,40,43,42);(20,21,23,24)(22,25,26,27)(28,29)(30,32)(31,33)(34,35)(36,38)(37,40)(39,43)(41,42);(20,22,23,26)(21,25,24,27)(28,30,31,35)(29,32,33,34)(36,37)(38,40)(39,41)(42,43)

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, 1534);