Finite Group Databasebeta

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C₂₃×#3121 #15670740

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 47 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)(26,29)(27,28)(30,31)(34,40)(35,42)(37,44)(39,46)(41,43)(45,47);(25,28)(29,31)(32,33)(34,37)(35,39)(36,38)(40,44)(41,45)(42,46)(43,47);(32,34,36,41)(33,37,38,45)(35,43,42,40)(39,47,46,44);(24,26,27,30)(25,29,28,31)(33,38)(37,45)(39,46)(44,47)

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, 1853);