Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8⋊#11764049 |
| Fitting | C2×Q8×C137 ⋊ C8 |
| Sylow | C137 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2192 |
226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21627);