Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2177 |
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30767713, #30767714, #30767786, … |
| maximal normal subgroup of | #30767713, #30767714, #30767786, … |
| maximal quotient of | #30767580, #30767752, #30767754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6384);