Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×D137 |
| Fitting | C2×D8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C22×D8 |
338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #357×D137, #31782503, #361×D137, … |
| maximal normal subgroup of | #357×D137, #31782503, #361×D137, … |
| maximal quotient of | C2×#102×D137, C2×#107×D137, C4×D8×D137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1317);