Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #1888 |
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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=f,b^2=dfg,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #1888×D67, C2×#22560609, #30857404, … |
| maximal normal subgroup of | #1888×D67, C2×#22560609, #30857404, … |
| maximal quotient of | #30750488, #30750508, #30750762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4910);