Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C139 · Schur multiplier (H2) = C24×C4 |
| direct product | C139×#20748 |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 8896 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,16,14,17,12,21)(11,18,20,15,19,24,22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(2,5)(6,8);(9,11)(10,15)(12,22)(13,20)(14,19)(16,24)(17,23)(18,21);(1,3,4,7)(2,6,5,8)(11,19)(15,23)(18,24)(20,22)8896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 13736);