Finite Group Databasebeta

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C₂₃×#3196 #15670815

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

414 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)(34,38)(35,42)(36,45)(37,40)(39,41)(43,47)(44,46);(24,26)(25,28)(27,31)(29,30)(32,34,37,36)(33,38,40,45)(35,43,44,41)(39,42,47,46);(26,31)(28,30)(32,35,37,44)(33,39,40,47)(34,41,36,43)(38,46,45,42);(25,29)(28,30)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1928);