← Prev (#44544655) Next (#44544657) →
Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 138 points:
(4,6)(5,9)(7,8)(10,11)(13,17,18,34,16,30,31,14,15,23,25,20,21,47)(19,41,42,92,52,118,49,27,28,67,61,82,83,78)(22,36,53,60,29,73,74,24,33,58,37,44,45,106)(26,62,40,95,79,50,51,38,39,64,65,113,32,80)(35,89,88,90,108,48,76,55,56,57,125,126,46,77)(43,101,100,124,132,133,81,70,71,131,129,102,119,116)(54,123,69,127,111,105,114,86,87,99,94,138,107,115)(59,120,121,63,103,104,112,84,91,85,93,72,134,135)(66,98,122,128,117,109,110,68,97,130,96,136,75,137);(1,2)(3,11,6,9,8,7,5,4,10)(12,13,16,22,15,19,29,46,21,32,52,84,33,54,88,55,18,26,40,66,28,43,72,105,45,75,111,137,76,112,126,106,31,49,79,114,51,81,117,134,83,119,132,101,120,131,99,67,53,85,122,98,87,124,128,95,125,127,93,62,89,92,60,34,25,37,61,56,39,63,94,90,65,96,129,123,97,130,121,58,42,69,100,91,71,102,133,118,104,136,116,80,115,113,78,47,74,108,135,77,110,138,109,73,107,103,70,41,68,64,38,23,35,57,86,36,59,82,50,30,48,44,27,17,24,20,14)
Conjugacy classes & character table
246 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 38);
Finite Group Databasebeta