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C₂₃×#3540 #15671159

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1058 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)(26,30)(32,33)(34,41)(35,38)(36,44)(37,40)(39,45)(42,46)(43,47);(25,28)(29,31)(32,34,37,35)(33,38,40,41)(36,42,45,43)(39,46,44,47);(24,25)(26,29)(27,28)(30,31)(32,35,37,34)(33,38,40,41)(36,43,45,42)(39,46,44,47);(24,26)(25,29)(27,30)(28,31)(32,33)(34,41)(35,38)(36,39)(37,40)(42,47)(43,46)(44,45);(32,36,37,45)(33,39,40,44)(34,42,35,43)(38,46,41,47)

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, 2272);