Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #366×D67 |
| Fitting | #366×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#366 |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 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.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1415×D67, #1416×D67, #30776267, … |
| maximal normal subgroup of | #1415×D67, #1416×D67, #30776267, … |
| maximal quotient of | #1371×D67, #30767471, #30767510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6285);