Finite Group Databasebeta

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C₂₃×#2696 #15670315

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1428);