Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#17984151 |
| unambiguous semidirect product | D137⋊#103 |
| Fitting | C2×Q8×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#103 |
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
368 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984151, #103×#10587739, #31796561, … |
| maximal normal subgroup of | C4×#17984151, #103×#10587739, #31796561, … |
| maximal quotient of | C2×Q8⋊#11764047, #31796078, C2×#22578253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1538);