Finite Group Databasebeta

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C₂₃×#3107 #15670726

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

390 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)(32,33,35,39)(34,41,42,37)(36,38,44,40)(43,46,47,45);(25,28)(29,31)(32,34,35,42)(33,37,39,41)(36,43,44,47)(38,45,40,46);(33,38)(36,44)(37,45)(39,40)(41,46)(43,47);(24,26,27,30)(25,29,28,31)

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, 1839);