Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2008 |
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,h^b=h^66,d^c=dg,e^c=eg749 conjugacy classes — view the full character table.
| maximal subgroup of | #2008×D67, C2×#22561260, #30882836, … |
| maximal normal subgroup of | #2008×D67, C2×#22561260, #30882836, … |
| maximal quotient of | #30756137, #30756151, #30756165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5561);