Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1571 |
168 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 168 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=e,b^2=df,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^66,c^b=cg,h^b=h^66962 conjugacy classes — view the full character table.
| maximal subgroup of | #30749851, #30749852, #30749862, … |
| maximal normal subgroup of | #30749851, #30749852, #30749862, … |
| maximal quotient of | #30745308, #30747046, #30748681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3286);