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Aliases
Subgroups
456 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 185 points:
(1,2,4,3)(5,6)(7,15)(8,12)(9,21)(10,13)(11,17)(14,23)(16,29)(18,28)(19,27)(20,33)(22,25)(24,31)(26,32)(30,36)(34,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185);(5,7,10,18)(6,11,13,25)(8,16,19,30)(9,22,23,17)(12,24,27,35)(14,28,21,15)(20,34,32,31)(26,36,33,29);(1,3,4,2)(5,8,10,19)(6,12,13,27)(7,16,18,30)(9,20,23,32)(11,24,25,35)(14,26,21,33)(15,29,28,36)(17,31,22,34);(6,13)(8,19)(11,25)(14,21)(15,28)(16,30)(20,32)(31,34)
Conjugacy classes & character table
6556 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 1682);
Finite Group Databasebeta