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Aliases
Subgroups
360 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 125 points:
(1,2,5,4)(3,7,8,6)(9,10,12,16)(11,18,19,14)(13,15,21,17)(20,22,24,23)(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);(1,3)(2,6)(4,7)(5,8)(9,11)(10,14)(12,19)(13,20)(15,23)(16,18)(17,22)(21,24);(1,4,5,2)(3,7,8,6)(10,15)(11,19)(13,21)(14,22)(16,17)(18,23);(3,8)(6,7)(10,16)(11,19)(15,17)(20,24)
Conjugacy classes & character table
2929 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 2087);
Finite Group Databasebeta