Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1911 |
| unambiguous semidirect product | C3⋊(C3×D637) |
| Fitting, Hall | C32×C13×C49 ⋊ C2 |
| derived | C3×C13×C49 ⋊ C2×C3 |
| Hall | C13×C49 ⋊ C3×D3 |
| Hall | C32×C49 ⋊ D13 |
| Hall | C32×C13 ⋊ D49 |
| Sylow | C49 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3×D147 |
| Sylow | C32 ⋊ D637 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1911 |
| commutator, cosocle, hypocenter | C3×C13×C49 | C2×C3 |
| Frattini | C7 | C3×D273 |
| Fitting | C32×C13×C49 | C2 |
| socle | C32×C7×C13 | D7 |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
2871 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D147, C3×D39×D49, C3×D3×D637, … |
| maximal normal subgroup of | C3×D13×D147, C3×D39×D49, C3×D3×D637, … |
| maximal quotient of | C3×Dic1911, C2×C3×D1911 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 68);