Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C349 ⋊ C2 |
| Sylow | C349 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,349|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^348,d^b=de,f^c=f^3481229 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D349, C2×#26013666, #36374941, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D349, C2×#26013666, #36374941, … |
| maximal quotient of | #36374144, #36374147, #36374183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 173);