Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863664 |
| Fitting | C2×AGL(1,ℤ/8)×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#472 |
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
758 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16863664, #30862708, #30862729, … |
| maximal normal subgroup of | C4×#16863664, #30862708, #30862729, … |
| maximal quotient of | C2×#22559562, C2×#22559606, C2×#22559616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14215);