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Aliases
Subgroups
144 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 171 points:
(1,2,6,11,7,13,23,12)(3,14,16,29,18,31,17,25)(4,10,19,28,20,9,5,21)(8,24,26,32,27,22,30,15)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(1,3)(2,8)(4,15)(5,22)(6,16)(7,18)(9,25)(10,29)(11,26)(12,30)(13,27)(14,21)(17,23)(19,24)(20,32)(28,31);(1,4,6,19,7,20,23,5)(2,9,11,21,13,10,12,28)(3,15,16,24,18,32,17,22)(8,25,26,14,27,29,30,31)
Conjugacy classes & character table
4448 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 911);
Finite Group Databasebeta