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C₂₃×#3493 #15671112

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1040 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)(26,30)(28,31)(32,33)(34,39)(35,40)(36,44)(37,38)(41,45)(42,43)(46,47);(24,25,27,29)(26,28,30,31)(33,38)(35,39)(41,44)(43,46);(24,26)(25,28)(27,30)(29,31)(32,34,37,40)(33,39,38,35)(36,42,45,47)(41,46,44,43);(32,35,37,39)(33,40,38,34)(36,43,45,46)(41,47,44,42);(32,36)(33,41)(34,42)(35,43)(37,45)(38,44)(39,46)(40,47)

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, 2225);