Finite Group Databasebeta

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C₂₃×#1818 #15669437

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 51 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)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37,39,42,40,43,46,49)(38,41,45,48,44,47,50,51);(29,32)(33,35)(36,38)(37,41)(39,45)(40,44)(42,48)(43,47)(46,50)(49,51);(25,27)(28,30,31,34)(29,33,32,35)(38,44)(41,47)(45,50)(48,51)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 550);