Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#22579943 |
| unambiguous semidirect product | D277⋊#103 |
| Fitting | C2×Q8×C277 ⋊ C4 |
| Sylow | C277 ⋊ 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.
| transitive degree | μt(G) = 4432 |
718 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1538);