← Prev (#14523354) Next (#14523356) →
Dic515 #14523355
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 112 points:
(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112);(1,3,2,4)(6,9)(7,8)(11,112)(12,111)(13,110)(14,109)(15,108)(16,107)(17,106)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)
Polycyclic presentation:
2,5,103,2|a^2=d,b^a=b^4,c^a=c^102
Conjugacy classes & character table
518 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2060, 4);
Finite Group Databasebeta