Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#106×D67 |
| Fitting | C2×#106×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 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.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1383×D67, #1386×D67, #30772386, … |
| maximal normal subgroup of | #1383×D67, #1386×D67, #30772386, … |
| maximal quotient of | C2×#334×D67, #1566×D67, C2×#22558963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13080);