Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #343×D67 |
| Fitting | #343×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #1345×D67, #1346×D67, #30766035, … |
| maximal normal subgroup of | #1345×D67, #1346×D67, #30766035, … |
| maximal quotient of | #1280×D67, #30745426, #30745429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4244);