Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #343×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1821 |
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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,c^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^66,f^c=fg758 conjugacy classes — view the full character table.
| maximal subgroup of | #30766511, #30766515, #30766524, … |
| maximal normal subgroup of | #30766511, #30766515, #30766524, … |
| maximal quotient of | #30749153, #30749162, #30749168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4589);