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Dic436 #13182020
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 125 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,125)(19,124)(20,123)(21,122)(22,121)(23,120)(24,119)(25,118)(26,117)(27,116)(28,115)(29,114)(30,113)(31,112)(32,111)(33,110)(34,109)(35,108)(36,107)(37,106)(38,105)(39,104)(40,103)(41,102)(42,101)(43,100)(44,99)(45,98)(46,97)(47,96)(48,95)(49,94)(50,93)(51,92)(52,91)(53,90)(54,89)(55,88)(56,87)(57,86)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,75)(69,74)(70,73)(71,72)
Polycyclic presentation:
2^4,109|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^108,c^b=cd,e^b=e^108
Conjugacy classes & character table
439 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 31);
Finite Group Databasebeta