Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#11764049 |
| unambiguous semidirect product | (C2×#11764049)⋊C23 |
| Fitting | C24×C137 ⋊ C8 |
| Sylow | C137 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2192 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21746);