Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16863219 |
| Sylow | C67 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#16863219, #365×Dic67, #30771251, … |
| maximal normal subgroup of | C4×#16863219, #365×Dic67, #30771251, … |
| maximal quotient of | C2×#22558275, #30767389, #30767463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6279);