Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #361×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2192 |
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^66,d^b=df,f^b=fg,h^b=h^66,e^c=eg,h^c=h^66551 conjugacy classes — view the full character table.
| maximal subgroup of | #2192×D67, C2×#22562169, #31009788, … |
| maximal normal subgroup of | #2192×D67, C2×#22562169, #31009788, … |
| maximal quotient of | #30767963, #30767974, #30768307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6470);