Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | #368×D67 |
| Fitting | #368×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#368 |
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1417×D67, #30776284, #1419×D67, … |
| maximal normal subgroup of | #1417×D67, #30776284, #1419×D67, … |
| maximal quotient of | #1371×D67, #1372×D67, #30767413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6300);