Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#22578350 |
| unambiguous semidirect product | D137⋊#385 |
| Fitting | C2×C22⋊C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#385 |
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2192 |
736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20960);