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Aliases
Subgroups
178 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 135 points:
(1,2,4,8,5,7,11,14)(3,6,10,12,9,13,15,16)(17,18)(19,22)(20,24)(21,23)(25,29)(26,28)(27,30)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135);(1,3)(2,6)(4,10)(5,9)(7,13)(8,12)(11,15)(14,16)(17,19,20,25,21,26,27,31)(18,22,24,29,23,28,30,32);(2,7)(3,9)(8,14)(10,15)(18,23)(22,28)(24,30)(29,32)
Conjugacy classes & character table
5768 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 186);
Finite Group Databasebeta