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Dic324 #13046286
Aliases
Splittings
Subgroups
45 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 97 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,97)(19,96)(20,95)(21,94)(22,93)(23,92)(24,91)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)
Polycyclic presentation:
2^4,3^4|a^2=d,b^2=cd,c^2=d,e^3=f,f^3=g,g^3=h,b^a=bc,c^a=cd,e^a=e^2f^2g^2h^2,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2
Conjugacy classes & character table
327 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 4);
Finite Group Databasebeta