Finite Group DatabasebetaFinite Group Databasebeta| order | 16218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D159 |
| unambiguous semidirect product | C3⋊(C17×D159) |
| unambiguous semidirect product | C53⋊(C17×C3⋊D3) |
| Fitting, socle, Hall | C32×C17×C53 ⋊ C2 |
| derived, Hall | C32×C53 ⋊ C2×C17 |
| Hall | C17×C53 ⋊ C3⋊D3 |
| Hall | C32×C17 ⋊ D53 |
| Sylow | C53 ⋊ C17×C3⋊D3 |
| Sylow | C32 ⋊ C17×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊D159 |
| commutator, cosocle, hypocenter | C32×C53 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C53 | C2 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8109 |
4080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#14274231, #44569984, D3×C17×D159, … |
| maximal normal subgroup of | C17×#14274231, #44569984, D3×C17×D159, … |
| maximal quotient of | C17×C3⋊Dic159, C2×C17×C3⋊D159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16218, 12);