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C₂₃×#3502 #15671121

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

964 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)(32,33,37,41)(34,39,35,38)(36,40,44,47)(42,46,43,45);(32,34,37,35)(33,38,41,39)(36,43,44,42)(40,46,47,45);(24,26,27,31)(25,28,29,30)(32,35,37,34)(33,39,41,38)(36,43,44,42)(40,46,47,45);(32,36,37,44)(33,40,41,47)(34,42,35,43)(38,45,39,46);(32,33)(34,38)(35,39)(36,40)(37,41)(42,45)(43,46)(44,47)

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, 2234);