Finite Group Databasebeta

?

← Prev (#68028) Next (#68030) →

#1840⋊C₃ #68029

• solvable

Aliases

Splittings

Subgroups

51 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 48 points:

(1,7,40,8,16,23,18,25,36,2,14,44,6,12,33,10,3,31,4,24,13,11,22,41)(5,28,48,27,37,43,20,26,47,9,15,42,21,39,34,30,19,46,17,32,35,29,38,45);(1,20)(2,27)(3,19)(4,5)(6,17)(7,28)(8,29)(9,10)(11,30)(12,39)(13,33,36,40)(14,15)(16,37)(18,21)(22,38)(23,44,31,41)(24,32)(25,26)(34,35,48,47)(42,43,45,46)

Polycyclic presentation:

2,3,2^6|a^2=c,c^2=h,d^2=fgh,e^2=fh,b^a=bg,d^a=df,e^a=eg,d^b=deg,e^b=d,f^b=fg,g^b=f,e^d=eh

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 605);