Finite Group Databasebeta

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C₂₃×#3095 #15670714

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

410 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)(32,33,37,41)(34,42,44,47)(35,40,36,39)(38,45,46,43);(25,28)(29,31);(24,26,27,30)(25,29,28,31)(32,34)(33,38)(35,43)(36,45)(37,44)(39,42)(40,47)(41,46);(32,35,37,36)(33,39,41,40)(34,43,44,45)(38,42,46,47)

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, 1827);