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Aliases
Subgroups
132 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 177 points:
(1,2)(3,6)(4,5)(7,8)(9,10,16,22)(11,18,26,37)(12,17,28,35)(13,20,30,32)(14,19,23,38)(15,31,29,21)(24,36,39,34)(25,40,27,33)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(2,5)(6,8)(9,11,23,39,15,25,13,12,16,26,14,24,29,27,30,28)(10,17,32,40,21,34,19,18,22,35,20,33,31,36,38,37);(1,3,4,7)(2,6,5,8)(9,12,13,27,29,39,23,26,16,28,30,25,15,24,14,11)(10,18,19,36,31,40,32,35,22,37,38,34,21,33,20,17)
Conjugacy classes & character table
3562 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 977);
Finite Group Databasebeta