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Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 141 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,21)(20,24)(22,27)(23,30)(25,33)(26,32)(28,37)(29,40)(31,42)(34,46)(35,45)(36,44)(38,51)(39,54)(41,56)(43,58)(47,63)(48,62)(49,61)(50,60)(52,69)(53,72)(55,74)(57,76)(59,78)(64,84)(65,83)(66,82)(67,81)(68,80)(70,71)(73,91)(75,93)(77,95)(79,97)(85,98)(86,102)(87,101)(88,100)(89,99)(90,107)(92,109)(94,111)(96,113)(103,114)(104,117)(105,116)(106,115)(108,121)(110,123)(112,125)(118,126)(119,128)(120,127)(122,131)(124,133)(129,134)(130,135)(132,137)(136,138)(139,140,141);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,32,61,101,128,138,130,105,67,36,21,24,45,82,117,134,132,120,88,50,27,30,33,62,102,126,124,122,106,68,37,40,42,46,83,114,112,110,108,89,51,54,56,58,63,98,96,94,92,90,69,72,74,76,78,84,79,77,75,73,71,70,91,93,95,97,64,59,57,55,53,52,107,109,111,113,85,47,43,41,39,38,99,121,123,125,103,65,34,31,29,28,80,115,131,133,118,86,48,25,23,22,60,100,127,137,129,104,66,35,20,19,44,81,116,135,136,119,87,49,26)
Conjugacy classes & character table
3090 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12342, 4);
Finite Group Databasebeta