Finite Group DatabasebetaFinite Group Databasebeta| order | 30366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C241 · Schur multiplier (H2) = C1 |
| direct product | D7⋊C9×C241 |
| unambiguous semidirect product | D7⋊(C9×C241) |
| unambiguous semidirect product | (C7⋊C9)⋊(C2×C241) |
| derived, Sylow | C7 ⋊ C2×C9×C241 |
| Hall | C7⋊C9×C241 ⋊ C2 |
| Hall | D7×C241 ⋊ C9 |
| Hall | C7×C241 ⋊ C2×C9 |
| Hall | C7⋊C9 ⋊ C2×C241 |
| Hall | D7 ⋊ C9×C241 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15183 |
5061 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30366, 18);