Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D4⋊C8×D67 |
| Fitting | D4⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C2×D4⋊C8×D67, #1476×D67, #1478×D67, … |
| maximal normal subgroup of | C2×D4⋊C8×D67, #1476×D67, #1478×D67, … |
| maximal quotient of | #1270×D67, #1271×D67, #30743767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2881);