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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 164 points:
(4,5)(6,7)(8,9)(10,11)(12,13)(15,19,20,38,43,16,17,25,27,66)(18,32,33,97,101,22,23,54,56,137)(21,48,49,50,77,29,30,87,88,90)(24,61,62,42,115,35,36,94,74,75)(26,71,72,129,96,40,41,86,118,113)(28,81,82,78,79,45,46,83,44,89)(31,92,93,155,142,51,52,134,135,124)(34,106,107,37,110,58,59,146,63,64)(39,114,76,67,65,68,69,121,105,111)(47,127,126,143,136,84,85,157,102,162)(53,99,100,149,150,95,55,140,109,164)(57,144,98,123,108,103,104,139,80,60)(70,73,152,138,91,112,116,119,163,132)(117,158,120,141,151,153,133,145,154,131)(122,125,159,160,161,156,147,128,130,148);(1,2)(3,4,6,8,10,12,13,11,9,7,5)(14,15,18,24,37,65,112,68,20,28,47,86,130,159,127,139,33,57,105,27,44,80,124,137,62,92,36,49,89,131,149,108,58,32,55,93,136,163,56,102,69,115,150,100,141,129,107,148,119,155,153,41,73,120,144,156,121,74,40,17,21,31,53,96,43,77,110,30,50,91,133,157,82,81,125,59,106,147,46,83,126,158,132,88,48,64,90,66,113,95,51,29,19,26,42,76,122,104,145,116,71,117,135,152,161,146,118,154,140,164,75,114,143,97,138,162,134,99,23,34,60,109,151,79,87,61,52,94,101,142,123,78,38,67,103,54,98,85,128,160,72,84,45,25,39,70,111,63,35,22,16)
Conjugacy classes & character table
400 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33220, 56);
Finite Group Databasebeta