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C₂₃×#3524 #15671143

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1030 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)(25,28)(29,31)(33,34)(36,44)(38,40)(42,47);(32,33,37,34)(35,40,43,38)(36,39,44,41)(42,46,47,45);(24,25)(26,29)(27,28)(30,31)(32,34,37,33)(35,40,43,38)(36,41,44,39)(42,46,47,45);(32,35,37,43)(33,38,34,40)(36,42,44,47)(39,45,41,46);(24,26,27,30)(25,29,28,31)(32,36)(33,39)(34,41)(35,42)(37,44)(38,45)(40,46)(43,47)

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, 2256);