Finite Group DatabasebetaFinite Group Databasebeta| order | 27180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C151 · Schur multiplier (H2) = C1 |
| direct product | C151×Dic45 |
| unambiguous semidirect product | C9⋊(Dic5×C151) |
| derived, Hall | C5×C9 ⋊ C4×C151 |
| Hall | C5×C9×C151 ⋊ C4 |
| Hall | C9×C151 ⋊ Dic5 |
| Hall | C5×C151 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic5×C151 |
| Sylow | C5 ⋊ Dic9×C151 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27180 |
7248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27180, 10);