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Aliases
Subgroups
1424 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 135 points:
(1,2)(3,12)(4,8)(5,9)(6,11)(7,15)(10,19)(13,26)(14,21)(16,25)(17,22)(18,23)(20,29)(24,30)(27,32)(28,31)(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)(2,7)(4,13)(5,14)(6,16)(8,20)(9,12)(10,25)(11,21)(15,19)(17,27)(18,28)(22,31)(23,26)(24,32)(29,30);(1,4)(2,8)(3,13)(5,18)(6,17)(7,20)(9,23)(10,24)(11,22)(12,26)(14,28)(15,29)(16,27)(19,30)(21,31)(25,32);(4,17)(8,22)(13,27)(18,30)(20,31)(23,24)(26,32)(28,29);(1,5,6,19)(2,9,11,10)(3,14,16,15)(4,18,17,30)(7,12,21,25)(8,23,22,24)(13,28,27,29)(20,26,31,32)
Conjugacy classes & character table
4532 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2316);
Finite Group Databasebeta