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C₂₃×#3504 #15671123

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(24,25,27,29)(26,30,31,28)(32,33)(34,38)(35,42)(36,37)(39,43)(40,46)(41,44)(45,47);(33,37)(38,44)(39,42)(45,46);(24,26,27,31)(25,28,29,30)(32,34,36,41)(33,38,37,44)(35,40,43,47)(39,45,42,46);(32,33)(34,38)(35,39)(36,37)(40,45)(41,44)(42,43)(46,47);(32,35,36,43)(33,39,37,42)(34,40,41,47)(38,45,44,46)

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, 2236);