Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #356×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2203 |
216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^66,d^b=dg,e^b=efg,d^c=df,e^c=eg,h^c=h^66,e^d=eg446 conjugacy classes — view the full character table.
| maximal subgroup of | #2203×D67, C2×#22562231, #31009994, … |
| maximal normal subgroup of | #2203×D67, C2×#22562231, #31009994, … |
| maximal quotient of | #30767900, #30767907, #30767908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6532);