Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#16840679 |
| Fitting | C22×Q16×C61 ⋊ C4 |
| Sylow | C61 ⋊ C22×#360 |
1214 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3904 |
484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1113621);