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D7105 #28382563
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 83 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)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(2,5)(3,4)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)
Polycyclic presentation:
2,5,7,29,7|c^7=e^6,b^a=b^4,c^a=c^6e,d^a=d^28,e^a=e^6
Conjugacy classes & character table
3554 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14210, 9);
Finite Group Databasebeta