Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#26042289 |
| unambiguous semidirect product | D181⋊#427 |
| Fitting | C22×C8×C181 ⋊ C4 |
| Sylow | C181 ⋊ C2×#427 |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 21161);