Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1482 |
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,d^b=df,h^b=h^66,h^c=h^66962 conjugacy classes — view the full character table.
| maximal subgroup of | #1482×D67, C2×#22558616, #30822340, … |
| maximal normal subgroup of | #1482×D67, C2×#22558616, #30822340, … |
| maximal quotient of | #30744172, #30744175, #30744182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2917);