Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×D268 |
| Fitting | C4×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
959 conjugacy classes — view the full character table.
| maximal subgroup of | #30769254, #30769258, #30769282, … |
| maximal normal subgroup of | #30769254, #30769258, #30769282, … |
| maximal quotient of | #30845183, #30845198, #30845213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16186);