Finite Group Databasebeta

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#1308⋊C₃ #67429

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

3,2^7|b^2=d,c^2=f,d^2=h,e^2=h,f^2=gh,b^a=cegh,c^a=bcdeh,d^a=fg,e^a=defg,f^a=efg,g^a=h,h^a=gh,c^b=cdeh,e^b=eg,f^b=fh,d^c=dg,e^c=egh

Conjugacy classes & character table

14 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5);