Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863837 |
| Fitting | C22×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
956 conjugacy classes — view the full character table.
| maximal subgroup of | #30772962, #30772968, #30772983, … |
| maximal normal subgroup of | #30772962, #30772968, #30772983, … |
| maximal quotient of | C2×#22561929, C2×#22561919, C2×#22561995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17639);