Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2223 |
144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 144 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|b^2=dfg,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^b=h^66,e^c=eg554 conjugacy classes — view the full character table.
| maximal subgroup of | #2223×D67, C2×#22562337, #31010404, … |
| maximal normal subgroup of | #2223×D67, C2×#22562337, #31010404, … |
| maximal quotient of | #30770045, #30770062, #30770096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6638);