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Dic213 #11719974
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 78 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);(1,3,2,4)(6,7)(9,78)(10,77)(11,76)(12,75)(13,74)(14,73)(15,72)(16,71)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,61)(27,60)(28,59)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)
Polycyclic presentation:
2^2,3,71|a^2=b,c^a=c^2,d^a=d^70
Conjugacy classes & character table
216 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(852, 3);
Finite Group Databasebeta