Finite Group Databasebeta

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C₂₃×#2161 #15669780

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,33,30,34,29,44)(26,35,39,51,37,49,40,54)(27,41,42,48,43,55,36,32)(31,45,47,53,46,52,50,38);(24,26,36,52,29,40,43,53,30,37,42,45,28,39,27,38)(25,31,41,51,33,47,48,49,34,46,55,54,44,50,32,35);(26,37)(31,46)(35,49)(38,53)(39,40)(45,52)(47,50)(51,54)

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, 893);