Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #354×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2201 |
226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^66,c^b=cg,e^b=efg,h^b=h^66,d^c=df,h^c=h^66,e^d=eg446 conjugacy classes — view the full character table.
| maximal subgroup of | #30776578, #30776580, #30776585, … |
| maximal normal subgroup of | #30776578, #30776580, #30776585, … |
| maximal quotient of | #30767890, #30767925, #30768059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6525);