Finite Group Databasebeta

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#1843⋊C₃ #68031

• solvable

Aliases

Splittings

Subgroups

61 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 44 points:

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

Polycyclic presentation:

2,3,2^6|a^2=ch,c^2=h,d^2=f,e^2=g,b^a=bgh,d^a=dfh,e^a=egh,d^b=def,e^b=df,f^b=fgh,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, 607);