Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14523989 |
| Sylow | C67 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30767562, C8×#14523989, #30767574, … |
| maximal normal subgroup of | #30767562, C8×#14523989, #30767574, … |
| maximal quotient of | C8×#14523989, #30767745, #30767747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6367);