Finite Group Databasebeta

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C₂₃×#2685 #15670304

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

666 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)(28,29,31,32)(30,33,34,35)(36,37,39,42)(38,41,43,40);(25,27)(29,32)(30,34)(36,38,39,43)(37,40,42,41);(24,25)(26,27)(28,29)(30,33)(31,32)(34,35)(36,38)(37,41)(39,43)(40,42);(28,30)(29,33)(31,34)(32,35)(36,37)(38,41)(39,42)(40,43)

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, 1417);