Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C11 |
| direct product | C19×C3⋊(C11⋊Dic11) |
| unambiguous semidirect product | C3⋊(C19×C11⋊Dic11) |
| unambiguous semidirect product | C11⋊(C19×Dic33) |
| derived, Hall | C3×C112 ⋊ C4×C19 |
| Hall | C3×C112×C19 ⋊ C4 |
| Hall | C112×C19 ⋊ Dic3 |
| Sylow | C112 ⋊ Dic3×C19 |
| Hall | C3×C19 ⋊ C11⋊Dic11 |
| Sylow | C3 ⋊ C19×C11⋊Dic11 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
6954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 53);