Finite Group Databasebeta

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C₂₃×#3168 #15670787

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(26,29)(27,28)(30,31)(32,33)(34,38)(35,42)(36,45)(37,40)(39,43)(41,46)(44,47);(25,28)(29,31)(32,34,37,36)(33,38,40,45)(35,41,44,43)(39,42,46,47);(32,35,36,43,37,44,34,41)(33,39,38,42,40,46,45,47);(24,26,27,30)(25,29,28,31)

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, 1900);