Finite Group DatabasebetaFinite Group Databasebeta| order | 18318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D129 |
| unambiguous semidirect product | C3⋊(C71×D43) |
| unambiguous semidirect product | C43⋊(D3×C71) |
| Fitting, socle, Hall | C3×C43×C71 ⋊ C2 |
| derived, Hall | C3×C43 ⋊ C2×C71 |
| Hall | C43×C71 ⋊ D3 |
| Hall | C3×C71 ⋊ D43 |
| Sylow | C43 ⋊ D3×C71 |
| Sylow | C3 ⋊ C71×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D129 |
| commutator, cosocle, hypocenter | C3×C43 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C71 | C2 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9159 |
4686 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D129, D3×C71×D43, D129⋊D71, … |
| maximal normal subgroup of | D71×D129, D3×C71×D43, D129⋊D71, … |
| maximal quotient of | C71×Dic129, C2×C71×D129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18318, 8);