Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16863393 |
| Fitting | C23×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#416 |
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761331, #30761337, #30761352, … |
| maximal normal subgroup of | #30761331, #30761337, #30761352, … |
| maximal quotient of | C2×#22558592, C2×#22558644, #30822244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13007);