Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #357×D67 |
| Fitting | #357×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#357 |
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#357×D67, #2138×D67, #2140×D67, … |
| maximal normal subgroup of | C2×#357×D67, #2138×D67, #2140×D67, … |
| maximal quotient of | #1331×D67, #30765804, #30765856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6206);