Finite Group Databasebeta

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C₂₃×#2381 #15670000

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(29,32)(30,34)(37,41)(38,44)(43,46)(45,50);(29,32)(33,35)(36,37,40,41)(38,42,44,48)(39,46,47,43)(45,51,50,49);(28,29,31,32)(30,33,34,35)(36,38)(37,42)(39,45)(40,44)(41,48)(43,49)(46,51)(47,50);(28,30)(29,33)(31,34)(32,35)(36,39,40,47)(37,43,41,46)(38,45,44,50)(42,49,48,51)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1113);