Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ #1422 |
58 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)(3,24)(4,7)(5,34)(6,35)(8,11)(9,53)(10,54)(12,15)(13,16)(14,76)(17,89)(18,21)(19,86)(20,47)(22,26)(23,27)(25,39)(28,74)(29,32)(30,56)(31,51)(33,36)(37,78)(38,40)(41,75)(42,45)(43,46)(44,80)(48,57)(49,50)(52,59)(55,92)(58,64)(60,95)(61,63)(62,83)(65,94)(66,68)(69,72)(70,73)(71,84)(77,81)(79,90)(82,85)(87,97)(88,96)(91,93)(98,100,101,112,105,114,104,103)(99,106,107,111,110,109,115,123)(102,113,116,120,119,127,118,117)(108,121,122,126,125,124,128,129);(2,3,5,9,6,10,14,25,4,8,12,22,13,23,33,52)(7,17,19,47,20,48,21,45,18,46,40,85,49,84,51,68)(11,28,30,67,31,38,71,75,29,66,69,76,70,15,37,39)(16,41,43,87,44,53,88,89,42,32,27,64,35,74,65,96)(24,55,57,73,58,63,93,59,56,90,91,72,92,95,97,94)(26,60,62,80,34,77,79,50,61,86,36,81,78,54,82,83)(98,99,102,108,103,109,117,124,104,107,118,122,114,123,127,129,105,110,119,125,112,106,120,121,101,115,116,128,100,111,113,126)Polycyclic presentation:
2^7,97|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^8,h^b=h^96,h^d=h^64,h^e=h^22,h^f=h^96104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21790);