Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #1400 |
74 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)(99,104)(100,108)(106,115)(107,116)(109,120)(110,121)(119,126)(122,128);(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)(98,99,100,105,101,106,109,117,102,107,110,118,111,119,122,127,103,104,108,114,112,115,120,124,113,116,121,125,123,126,128,129)Polycyclic presentation:
2^7,97|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^8,d^b=dg,h^b=h^96,h^d=h^64,h^e=h^22,h^f=h^9692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21784);