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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)(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);(3,4,7,12,9,13,8,23)(5,14,17,29,19,30,18,33)(6,20,21,27,22,34,15,11)(10,24,25,32,26,31,28,16);(3,5,15,31,8,18,22,32,9,19,21,24,7,17,6,16)(4,10,20,29,12,25,27,30,13,26,34,33,23,28,11,14)
Conjugacy classes & character table
6028 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 892);
Finite Group Databasebeta