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Cayley diagramAliases
Splittings
Subgroups
100 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 64 points:
(1,2,7,12)(3,14,18,30)(4,19,15,9)(5,33,6,35,22,36,24,34,25,10,23,11)(8,26,29,13)(16,63,17,57,43,58,45,64,46,39,44,40)(20,60,21,31,49,32,41,59,42,47,50,48)(27,62,28,37,53,38,55,61,56,51,54,52);(1,23,7,22)(2,54,12,53)(3,62,18,61)(4,49,15,50)(5,25,24,6)(8,34,29,33)(9,63,19,64)(10,56,35,28)(11,27,36,55)(13,44,26,43)(14,59,30,60)(16,52,45,38)(17,37,46,51)(20,21,41,42)(31,40,47,58)(32,57,48,39)
Polycyclic presentation:
2^2,3,2^5|b^2=h,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, 5857);
Finite Group Databasebeta