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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 158 points:
(1,2)(3,4,5,6,7)(9,10,12)(11,14,19)(13,17,16)(15,21,29)(18,24,26)(20,27,23)(22,31,42)(25,34,39)(28,37,36)(30,40,33)(32,44,58)(35,47,55)(38,50,52)(41,53,49)(43,56,46)(45,60,77)(48,63,74)(51,66,71)(54,69,68)(57,72,65)(59,75,62)(61,79,98)(64,80,95)(67,84,92)(70,87,89)(73,90,86)(76,93,83)(78,96,81)(82,101,116)(85,103,113)(88,105,110)(91,108,107)(94,111,104)(97,114,102)(99,117,100)(106,121,128)(109,123,125)(112,126,122)(115,129,120)(118,131,119)(124,135,139)(127,137,136)(130,140,134)(132,142,133)(138,146,147)(141,148,145)(143,150,144)(149,154,153)(151,155,152)(156,158,157);(8,9,11,15,22,32,45,61,80,44,59,76,94,112,127,138,142,114,75,42,55,71,89,107,122,134,144,146,123,87,50,24,10,13,18,25,35,48,64,82,101,60,78,97,115,130,141,149,150,129,93,56,29,39,52,68,86,104,120,133,135,105,66,34,14,20,28,38,51,67,85,98,116,79,99,118,132,143,151,156,155,140,111,72,40,19,26,36,49,65,83,102,119,121,84,47,21,30,41,54,70,88,106,117,77,95,113,128,139,147,153,157,158,148,126,90,53,27,12,16,23,33,46,62,81,100,103,63,31,43,57,73,91,109,124,131,96,58,74,92,110,125,136,145,152,154,137,108,69,37,17)
Conjugacy classes & character table
530 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4530, 3);
Finite Group Databasebeta