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Aliases
Subgroups
128 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 173 points:
(1,2)(3,4)(5,6,9,14,11,17,23,16)(7,18,20,32,22,33,34,27)(8,15,10,13,24,30,25,31)(12,21,26,35,29,36,28,19)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173);(2,4)(5,7,10,21,9,20,24,35,11,22,25,36,23,34,8,19)(6,12,15,27,16,28,31,33,17,29,30,32,14,26,13,18)
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, 113);
Finite Group Databasebeta