Finite Group Databasebeta

?

← Prev (#15670908) Next (#15670910) →

C₂₃×#3290 #15670909

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

454 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)(26,35)(27,32)(28,45)(29,34)(30,38)(31,43)(33,46)(36,48)(37,54)(39,50)(40,49)(41,47)(42,52)(44,51)(53,55);(24,26)(25,30)(27,41)(28,39)(29,40)(31,48)(32,53)(33,49)(34,50)(35,45)(36,44)(37,42)(38,46)(43,55)(47,52)(51,54);(24,27)(25,31)(26,36)(28,42)(29,44)(30,47)(32,45)(33,51)(34,52)(35,54)(37,38)(39,55)(40,41)(43,46)(48,50)(49,53);(24,27)(25,32)(26,37)(28,43)(29,44)(30,48)(31,45)(33,52)(34,51)(35,54)(36,38)(39,41)(40,55)(42,46)(47,50)(49,53)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2022);