Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#17984117 |
| Fitting | C2×SD16×C137 ⋊ C2 |
| Sylow | C137 ⋊ 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.
974 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984117, #31789611, #31789625, … |
| maximal normal subgroup of | C4×#17984117, #31789611, #31789625, … |
| maximal quotient of | C2×#22577410, C2×#22577401, C2×#22577442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1340);