Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#100×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1911 |
362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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=df,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,e^b=eg,h^b=h^66,d^c=dg,f^c=fg755 conjugacy classes — view the full character table.
| maximal subgroup of | #30771587, #30771592, #30771594, … |
| maximal normal subgroup of | #30771587, #30771592, #30771594, … |
| maximal quotient of | #30751324, #30751334, #30751344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5040);