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Aliases
Subgroups
452 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 181 points:
(1,2,6,11,7,10,5,19)(3,12,14,8,15,23,20,22)(4,9,18,24,16,25,17,29)(13,26,28,21,27,31,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181);(1,3)(2,8)(4,13)(5,20)(6,14)(7,15)(9,21)(10,22)(11,23)(12,19)(16,27)(17,30)(18,28)(24,31)(25,32)(26,29);(1,4,6,18,7,16,5,17)(2,9,11,24,10,25,19,29)(3,13,14,28,15,27,20,30)(8,21,23,31,22,32,12,26);(2,10)(4,16)(8,22)(11,19)(12,23)(13,27)(17,18)(28,30)
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, 1689);
Finite Group Databasebeta