Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 326 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^66,e^c=eg956 conjugacy classes — view the full character table.
| maximal subgroup of | #2023×D67, C2×#22561343, #30883124, … |
| maximal normal subgroup of | #2023×D67, C2×#22561343, #30883124, … |
| maximal quotient of | #30758799, #30758809, #30758839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5644);