Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213×C4 |
| direct product | C23×#14519766 |
| Fitting | C24×Q8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C23×#124 |
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
2512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1076232);