Finite Group DatabasebetaFinite Group Databasebeta| order | 30366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C241 · Schur multiplier (H2) = C1 |
| direct product | D63×C241 |
| unambiguous semidirect product | C7⋊(D9×C241) |
| unambiguous semidirect product | C9⋊(D7×C241) |
| Fitting, Hall | C7×C9×C241 ⋊ C2 |
| derived, Hall | C7×C9 ⋊ C2×C241 |
| Hall | C9×C241 ⋊ D7 |
| Hall | C7×C241 ⋊ D9 |
| Sylow | C9 ⋊ D7×C241 |
| Sylow | C7 ⋊ D9×C241 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C241 | D63 |
| commutator, cosocle, hypocenter | C7×C9 | C2×C241 |
| Frattini | C3 | D21×C241 |
| Fitting | C7×C9×C241 | C2 |
| socle | C3×C7×C241 | D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C241 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15183 |
7953 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30366, 11);