Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊(D49⋊C3) |
| unambiguous semidirect product | C3⋊(C13×D49⋊C3) |
| unambiguous semidirect product | (C49⋊C3)⋊(D3×C13) |
| unambiguous semidirect product | D147⋊(C3×C13) |
| Fitting | C3×C13×C49 ⋊ C2×C3 |
| derived | C3×C49 ⋊ C2×C3×C13 |
| Hall | C3×C13×C49⋊C3 ⋊ C2 |
| Hall | C13×C49 ⋊ C3×D3 |
| Hall | C3×C49⋊C3 ⋊ C2×C13 |
| Sylow | C49 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊(D49⋊C3) |
| commutator, cosocle, hypocenter | C3×C49 | C2×C3×C13 |
| Frattini | C7 | C13×C3⋊AGL(1,𝔽7) |
| Fitting | C3×C13×C49 | C2×C3 |
| socle | C3×C7×C13 | AGL(1,𝔽7) |
| LCS | G ▷ C3×C49 | |
| UCS | C1 ◁ C13 | |
54 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 52);