Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22579906 |
| Fitting | C22×D4×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 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.
| transitive degree | μt(G) = 4432 |
2782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983540, #47983546, #47983644, … |
| maximal normal subgroup of | #47983540, #47983546, #47983644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1336);