Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2076 |
256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 256 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=e,c^2=dg,e^2=g,b^a=bd,c^a=ce,h^a=h^66,c^b=cf,e^c=eg956 conjugacy classes — view the full character table.
| maximal subgroup of | #2076×D67, C2×#22561640, #30884674, … |
| maximal normal subgroup of | #2076×D67, C2×#22561640, #30884674, … |
| maximal quotient of | #30760539, #30760549, #30760573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5941);