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Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 128 points:
(1,2,3)(5,8,9,19)(6,13,14,36)(7,17,18,48)(10,25,26,37)(11,29,30,20)(12,33,34,82)(15,42,43,47)(16,45,46,38)(21,55,56,90)(22,59,60,89)(23,61,40,95)(24,64,49,85)(27,69,70,63)(28,73,74,119)(31,78,66,116)(32,80,65,112)(35,87,88,51)(39,93,94,102)(41,44,50,100)(52,53,91,58)(54,81,57,109)(62,114,99,84)(67,98,96,111)(68,101,103,106)(71,113,118,117)(72,97,110,86)(75,120,121,92)(76,115,122,125)(77,83,104,124)(79,123,105,108)(107,128,127,126);(4,12,75,61,111,102,104,8,54,62,13,92,126,114,25,43,79,29,51,115,42,69,96,74,9,7,35,78,113,71,50,11,22,83,55,39,101,123,53,66,44,91,76,64,109,46,40,110,26,24,17,89,103,27,86,6,32,33,112,107,45,119,21,56,73,38,127,80,82,65,14,97,70,68,59,48,49,10,72,23,16,81,85,122,52,100,31,58,108,106,94,90,124,60,30,41,118,117,116,88,18,5,28,67,63,47,125,87,20,105,15,37,84,128,120,36,99,57,19,77,93,98,95,121,34)
Conjugacy classes & character table
105 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 5);
Finite Group Databasebeta