Finite Group DatabasebetaFinite Group Databasebeta| order | 7434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1239 |
| unambiguous semidirect product | C7⋊(C3⋊D177) |
| unambiguous semidirect product | C59⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C59 ⋊ C2 |
| Hall | C32×C59 ⋊ D7 |
| Hall | C7×C59 ⋊ C3⋊D3 |
| Hall | C32×C7 ⋊ D59 |
| Sylow | C59 ⋊ C3⋊D21 |
| Sylow | C32 ⋊ D413 |
| Sylow | C7 ⋊ C3⋊D177 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C59 | C2 |
| LCS | G ▷ C32×C7×C59 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,59|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^581860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×C3⋊D21, D7×C3⋊D177, C3⋊D3×D413, … |
| maximal normal subgroup of | D59×C3⋊D21, D7×C3⋊D177, C3⋊D3×D413, … |
| maximal quotient of | C3⋊Dic1239, C2×C3⋊D1239, C5×C3⋊D1239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7434, 32);