Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD16×#11764308 |
| Fitting | SD16×C277 ⋊ C4 |
| Sylow | C277 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2216 |
511 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1586);