Finite Group Databasebeta

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C₂₃×#3097 #15670716

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 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)(32,33,36,40)(34,37,41,45)(35,38,43,39)(42,44,47,46);(25,28)(29,31)(32,34)(33,37)(35,42)(36,41)(38,44)(39,46)(40,45)(43,47);(24,26,27,30)(25,29,28,31)(33,38)(35,43)(37,44)(39,40)(42,47)(45,46);(34,41)(37,45)(42,47)(44,46)

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, 1829);