Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C337 ⋊ C2 |
| Sylow | C337 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^336,d^b=de,f^c=f^3361187 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D337, C2×#24924986, #36342102, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D337, C2×#24924986, #36342102, … |
| maximal quotient of | #36341305, #36341308, #36341344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 173);