Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C49 ⋊ C2 |
| Sylow | C49 ⋊ SD16 |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^4,7^2|b^2=d,c^2=d,e^7=f,b^a=bc,c^a=cd,e^a=e^6f^6,f^a=f^6,c^b=cd127 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D49, #13095943, #13095947, … |
| maximal normal subgroup of | SD16×D49, #13095943, #13095947, … |
| maximal quotient of | #13095848, #13095850, #13095876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 17);