Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×D277 |
| Fitting | C2×D8×C277 ⋊ C2 |
| Sylow | C277 ⋊ 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.
| transitive degree | μt(G) = 4432 |
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D277, #47984881, #361×D277, … |
| maximal normal subgroup of | #357×D277, #47984881, #361×D277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1317);