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Aliases
Subgroups
216 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 159 points:
(2,3)(5,6)(7,10)(8,9)(11,12)(13,14,16,19,17,20,23,26)(15,18,22,25,21,24,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159);(1,2,4,3)(6,9)(10,12)(13,15)(14,18)(16,22)(17,21)(19,25)(20,24)(23,27)(26,28);(1,3,4,2)(5,7,8,11)(6,10,9,12)(15,21)(18,24)(22,27)(25,28)
Conjugacy classes & character table
5764 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 564);
Finite Group Databasebeta