Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2065 |
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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=de,b^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^66,c^b=cf,d^c=dg,e^c=eg,f^c=fg,h^c=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2065×D67, C2×#22561582, #30884443, … |
| maximal normal subgroup of | #2065×D67, C2×#22561582, #30884443, … |
| maximal quotient of | #30760347, #30760368, #30760399, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5883);