Finite Group DatabasebetaFinite Group Databasebeta| order | 31168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #117×D487 |
| Fitting | #117×C487 ⋊ C2 |
| Sylow | C487 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7792 |
4900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31168, 1001);