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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 96 points:
(1,17,54,19,4,48,9,50,20,3,24,79)(2,34,73,37,11,65,15,68,38,10,43,92)(5,56,84,62,21,81,29,87,51,26,58,96)(6,60,53,7,22,86,8,23,52,31,32,61)(12,74,94,14,39,93,45,42,70,44,75,77)(13,69,85,35,40,90,30,66,71,36,59,89)(16,67,95,25,41,91,46,55,72,47,76,80)(18,63,88,27,49,83,33,57,78,28,64,82);(1,46)(2,3)(4,59)(5,37)(6,44)(7,30)(8,14)(9,16)(10,29)(11,32)(12,26)(13,31)(15,19)(17,74)(18,25)(20,93)(21,39)(22,43)(23,41)(24,40)(27,35)(28,36)(33,47)(34,56)(38,61)(42,50)(45,62)(48,71)(49,66)(51,89)(52,72)(53,95)(54,77)(55,63)(57,67)(58,75)(60,76)(64,69)(65,82)(68,87)(70,88)(73,86)(78,94)(79,85)(80,81)(83,92)(84,90)(91,96)
Polycyclic presentation:
2^2,3,2^5|a^2=h,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=g,g^c=fgh,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, 5856);
Finite Group Databasebeta