Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16863193 |
| Sylow | C67 ⋊ C2×#355 |
260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
950 conjugacy classes — view the full character table.
| maximal subgroup of | #30743576, #30743577, #30743600, … |
| maximal normal subgroup of | #30743576, #30743577, #30743600, … |
| maximal quotient of | C2×#22558141, C2×#22558153, #30765105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6188);