Finite Group Databasebeta

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#3417⋊C₃ #73282

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 64 points:

(2,8)(3,14)(4,15)(5,22,25)(6,24,23)(9,10)(11,53,37,27,34,56)(12,55,35,28,36,54)(13,29)(16,61,46,38,43,64)(17,63,44,39,45,62)(18,40)(19,26)(20,50,42,41,49,21)(30,59,52,32,57,48)(31,47,58,33,51,60);(1,35,7,34)(2,23,13,22)(3,54,18,53)(4,59,15,60)(5,37,24,12)(6,11,25,36)(8,44,29,43)(9,62,26,61)(10,49,19,50)(14,58,40,57)(16,56,45,28)(17,27,46,55)(20,33,41,48)(21,47,42,32)(30,64,51,39)(31,38,52,63)

Polycyclic presentation:

2^2,3,2^5|d^2=eh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=de,e^a=eh,d^b=de,e^b=eh,f^c=fgh,g^c=fh,g^f=gh

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5858);