Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1911 |
| unambiguous semidirect product | C13⋊(C3⋊D147) |
| unambiguous semidirect product | C49⋊(C3⋊D39) |
| Fitting, derived, Hall | C32×C13×C49 ⋊ C2 |
| 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 | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C13×C49 | C2 |
| Frattini | C7 | C3⋊D273 |
| socle | C32×C7×C13 | D7 |
| LCS | G ▷ C32×C13×C49 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,13,7|d^7=f^6,b^a=b^2,c^a=c^2,d^a=d^6f,e^a=e^12,f^a=f^62868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×C3⋊D147, D49×C3⋊D39, C3⋊D3×D637, … |
| maximal normal subgroup of | D13×C3⋊D147, D49×C3⋊D39, C3⋊D3×D637, … |
| maximal quotient of | C3⋊Dic1911, C2×C3⋊D1911 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 72);