Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C361 · Schur multiplier (H2) = C2 |
| direct product | C2×D21×C361 |
| unambiguous semidirect product | (C2×C3)⋊(D7×C361) |
| unambiguous semidirect product | (C2×C7)⋊(D3×C361) |
| Fitting | C2×C3×C7×C361 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C22×C361 |
| Hall | C3×C7×C361 ⋊ C22 |
| Hall | C7×C361 ⋊ C2×D3 |
| Hall | C3×C361 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C361 |
| Sylow | C3 ⋊ C2×D7×C361 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15162 |
8664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 63);