Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14268594 |
| Fitting, socle, derived | C3×C7×C43 ⋊ C2×C3 |
| Hall | C3×#11744749 ⋊ C2 |
| Hall | C7×C43 ⋊ C3×D3 |
| Sylow | C43 ⋊ C3⋊AGL(1,𝔽7) |
| Sylow | C7 ⋊ C3⋊(D43⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C43 | C2×C3 |
| LCS | G ▷ C3×C7×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,43|c^a=c^2,d^a=d^6,e^a=e^42,d^b=d^2,e^b=e^36159 conjugacy classes — view the full character table.
| maximal subgroup of | #14268588⋊D3, #14268592⋊D3, D3×#14268594, … |
| maximal normal subgroup of | #14268588⋊D3, #14268592⋊D3, D3×#14268594, … |
| maximal quotient of | C3⋊#16813407, C2×C3⋊#14268594, C5×C3⋊#14268594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 61);