Finite Group DatabasebetaFinite Group Databasebeta| order | 9030 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C7×C43 |
| unambiguous semidirect product | C3⋊(C2×C5×C7×C43) |
| Fitting, socle, Hall | C3×C5×C7×C43 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C7×C43 |
| Hall | C3×C7×C43 ⋊ C2×C5 |
| Hall | C3×C5×C43 ⋊ C2×C7 |
| Hall | C3×C43 ⋊ C2×C5×C7 |
| Hall | C3×C5×C7 ⋊ C2×C43 |
| Hall | C3×C7 ⋊ C2×C5×C43 |
| Hall | C3×C5 ⋊ C2×C7×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7×C43 | D3 |
| commutator, hypocenter | C3 | C2×C5×C7×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C43 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C5×C7×C43 | |
32 conjugacy classes of subgroups.
4515 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C7×D43, C5×D3×D7×C43, C5×D3×D301, … |
| maximal normal subgroup of | C5×D3×C7×D43, C5×D3×D7×C43, C5×D3×D301, … |
| maximal quotient of | C5×C7×Dic3×C43, C2×C5×D3×C7×C43, C5×C7×D9×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9030, 15);