Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16863209 |
| Sylow | C67 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 256 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.
956 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16863209, #361×Dic67, #30771101, … |
| maximal normal subgroup of | C4×#16863209, #361×Dic67, #30771101, … |
| maximal quotient of | C2×#22558176, #30765606, #30765837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6250);