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Aliases
Subgroups
364 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)(9,10,14,17)(11,15,13,21)(12,19,20,23)(16,22,24,18)(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)(9,11,14,13)(10,15,17,21)(12,18,20,22)(16,23,24,19);(1,4,5,2)(3,7,8,6)(9,12)(10,16)(11,18)(13,22)(14,20)(15,23)(17,24)(19,21);(3,8)(6,7)(9,11,14,13)(10,15,17,21)(12,18,20,22)(16,23,24,19)
Conjugacy classes & character table
3535 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 2073);
Finite Group Databasebeta