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C₂₃×#3516 #15671135

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1012 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)(33,36)(34,40)(39,43)(41,46);(32,33,37,36)(34,38,40,42)(35,43,44,39)(41,47,46,45);(24,25)(26,29)(27,28)(30,31)(32,34)(33,38)(35,41)(36,42)(37,40)(39,45)(43,47)(44,46);(32,35,37,44)(33,39,36,43)(34,41,40,46)(38,45,42,47);(24,26,27,30)(25,29,28,31)(32,36,37,33)(34,42,40,38)(35,43,44,39)(41,47,46,45)

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, 2248);