Finite Group Databasebeta

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#1780⋊C₃ #68025

• solvable

Aliases

Splittings

Subgroups

127 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 40 points:

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

Polycyclic presentation:

2,3,2^6|a^2=c,c^2=h,d^2=h,e^2=h,d^a=df,e^a=eg,d^b=deg,e^b=df,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, 601);