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D8109 #30633953
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 79 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(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);(2,9)(3,8)(4,7)(5,6)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(28,79)(29,78)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)
Polycyclic presentation:
2,3,17,53,3|b^3=e^2,b^a=b^2e,c^a=c^16,d^a=d^52,e^a=e^2
Conjugacy classes & character table
4056 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16218, 8);
Finite Group Databasebeta