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Aliases
Subgroups
792 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 125 points:
(1,2)(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);(3,4,5,6)(7,8)(9,16)(10,14)(11,19)(12,15)(13,17)(18,21)(20,22);(7,9)(8,13)(10,17)(11,20)(12,18)(14,21)(15,22)(16,19);(7,10,12,11)(8,14,15,19)(9,17,18,20)(13,21,22,16)
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, 1624);
Finite Group Databasebeta