Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ #1398 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3104 |
A minimal faithful permutation representation — 2 generators on 129 points:
(1,2,12,4)(3,18,66,45)(5,7,36,27)(6,13,29,15)(8,20,70,42)(9,11,48,38)(10,19,56,22)(14,58,51,16)(17,37,43,32)(21,40,72,81)(23,25,50,74)(24,49,28,31)(26,65,83,91)(30,54,59,55)(33,35,86,64)(34,44,69,60)(39,47,76,67)(41,71,90,46)(52,79,93,85)(53,57,61,63)(62,88,84,80)(68,87,94,77)(73,75,78,92)(82,89,96,95)(99,104,106,108)(100,109)(105,118,119,116)(107,117,121,122)(110,123)(111,115)(120,128,129,127)(124,126);(2,3,5,9,6,10,4,8)(7,14,16,33,17,34,15,32)(11,21,23,39,24,38,22,18)(12,26,13,30,28,53,27,52)(19,41,43,45,44,20,42,46)(25,50,51,75,36,64,31,58)(29,55,37,65,56,82,49,77)(35,59,61,68,62,67,60,40)(47,72,73,80,74,63,48,54)(57,84,86,81,78,66,85,71)(69,91,88,79,90,94,70,89)(76,83,87,96,93,97,92,95)(98,99,100,105,101,107,110,120,102,108,111,118,112,122,124,128,103,106,109,119,113,121,123,129,114,104,115,116,125,117,126,127)Polycyclic presentation:
2^7,97|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^50,c^b=cg,h^b=h^22,h^c=h^75,h^d=h^96,h^e=h^96236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21601);