Finite Group Databasebeta

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C₂₃×#3212 #15670831

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

400 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)(26,30)(27,29)(28,31)(32,33)(34,42)(35,41)(36,38)(37,40)(39,44)(43,47)(45,46);(24,26,27,31)(25,28,29,30)(33,38)(34,43)(40,41)(44,45);(26,31)(28,30)(32,34)(33,39)(35,44)(36,43)(37,45)(38,46)(40,42)(41,47);(25,29)(28,30)(32,35,36,37)(33,40,38,41)(34,44,43,45)(39,42,46,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1944);