Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C11 |
| direct product | C19×(C11⋊Dic11)⋊C3 |
| unambiguous semidirect product | (C11⋊Dic11)⋊(C3×C19) |
| derived, Sylow | C112 ⋊ C3×C4×C19 |
| Hall | C19×C11⋊Dic11 ⋊ C3 |
| Hall | C19×C112⋊C3 ⋊ C4 |
| Hall | C112×C19 ⋊ C3×C4 |
| Hall | C11⋊Dic11 ⋊ C3×C19 |
| Hall | C112⋊C3 ⋊ C4×C19 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2508 |
988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 43);