Finite Group DatabasebetaFinite Group Databasebeta| order | 8118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D123 |
| unambiguous semidirect product | C3⋊(C11×D123) |
| unambiguous semidirect product | C41⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C11×C41 ⋊ C2 |
| derived, Hall | C32×C41 ⋊ C2×C11 |
| Hall | C11×C41 ⋊ C3⋊D3 |
| Hall | C32×C11 ⋊ D41 |
| Sylow | C41 ⋊ C11×C3⋊D3 |
| Sylow | C32 ⋊ C11×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D123 |
| commutator, hypocenter | C32×C41 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C41 | C2 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
2046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C3⋊D3×D41, D11×C3⋊D123, D451⋊(C3⋊D3), … |
| maximal normal subgroup of | C11×C3⋊D3×D41, D11×C3⋊D123, D451⋊(C3⋊D3), … |
| maximal quotient of | C11×C3⋊Dic123, C2×C11×C3⋊D123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8118, 18);