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C₂₃×#3067 #15670686

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 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)(26,36)(27,41)(28,33)(29,34)(30,35)(31,38)(32,42)(37,51)(39,47)(40,46)(43,48)(44,49)(45,53)(50,52)(54,55);(24,26,28,38,30,40,29,39)(25,31,34,36,35,47,33,46)(27,37,42,52,43,53,44,54)(32,45,41,50,49,51,48,55);(24,27)(25,32)(26,37)(28,42)(29,44)(30,43)(31,45)(33,48)(34,41)(35,49)(36,50)(38,52)(39,54)(40,53)(46,55)(47,51);(24,28,30,29)(25,33,35,34)(26,38,40,39)(27,42,43,44)(31,46,47,36)(32,48,49,41)(37,52,53,54)(45,55,51,50)

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, 1799);