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C₂₃×#3552 #15671171

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1004 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)(26,27)(28,29)(30,31)(33,38)(34,35)(36,44)(46,47);(25,29)(26,30)(32,33,37,38)(34,40,35,39)(36,41,44,45)(42,47,43,46);(32,34,37,35)(33,39,38,40)(36,42,44,43)(41,46,45,47);(24,26,28,30)(25,27,29,31)(32,35,37,34)(33,40,38,39)(36,43,44,42)(41,47,45,46);(24,27)(25,30)(26,29)(28,31)(32,36)(33,41)(34,42)(35,43)(37,44)(38,45)(39,46)(40,47)

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, 2284);