Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D903 |
| unambiguous semidirect product | C7⋊(C3⋊D129) |
| unambiguous semidirect product | C43⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C43 ⋊ C2 |
| Hall | C32×C43 ⋊ D7 |
| Hall | C7×C43 ⋊ C3⋊D3 |
| Hall | C32×C7 ⋊ D43 |
| Sylow | C43 ⋊ C3⋊D21 |
| Sylow | C32 ⋊ D301 |
| Sylow | C7 ⋊ C3⋊D129 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C43 | C2 |
| LCS | G ▷ C32×C7×C43 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,43|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^421356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×C3⋊D21, D7×C3⋊D129, C3⋊D3×D301, … |
| maximal normal subgroup of | D43×C3⋊D21, D7×C3⋊D129, C3⋊D3×D301, … |
| maximal quotient of | C3⋊Dic903, C2×C3⋊D903, C5×C3⋊D903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 88);