Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×C3⋊D147 |
| unambiguous semidirect product | C3⋊(C13×D147) |
| unambiguous semidirect product | C49⋊(C13×C3⋊D3) |
| Fitting, Hall | C32×C13×C49 ⋊ C2 |
| derived, Hall | C32×C49 ⋊ C2×C13 |
| Hall | C13×C49 ⋊ C3⋊D3 |
| Hall | C32×C13 ⋊ D49 |
| Sylow | C49 ⋊ C13×C3⋊D3 |
| Sylow | C32 ⋊ C13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊D147 |
| commutator, cosocle, hypocenter | C32×C49 | C2×C13 |
| Frattini | C7 | C13×C3⋊D21 |
| Fitting | C32×C13×C49 | C2 |
| socle | C32×C7×C13 | D7 |
| LCS | G ▷ C32×C49 | |
| UCS | C1 ◁ C13 | |
72 conjugacy classes of subgroups.
2886 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×C3⋊D147, C13×C3⋊D3×D49, D637⋊(C3⋊D3), … |
| maximal normal subgroup of | D13×C3⋊D147, C13×C3⋊D3×D49, D637⋊(C3⋊D3), … |
| maximal quotient of | C13×C3⋊Dic147, C2×C13×C3⋊D147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 71);