Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16862275 |
| Fitting | C2×SD16×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
932 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16862275, #30674783, #30674797, … |
| maximal normal subgroup of | C4×#16862275, #30674783, #30674797, … |
| maximal quotient of | C2×#22553319, C2×#22553310, C2×#22553351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1340);