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Aliases
Subgroups
140 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 169 points:
(1,2,5,10,7,11,6,21)(3,12,16,28,14,26,17,31)(4,18,19,25,20,32,13,9)(8,22,24,30,23,29,27,15)(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);(1,3,13,29,6,17,20,30,7,14,19,22,5,16,4,15)(2,8,18,28,10,24,25,26,11,23,32,31,21,27,9,12);(3,14)(8,23)(12,26)(15,30)(16,17)(22,29)(24,27)(28,31)
Conjugacy classes & character table
4384 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 893);
Finite Group Databasebeta