Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16838466 |
| Fitting, socle, derived | C3×C72×C13 ⋊ C2×C3 |
| Hall | C3×C13×#3862 ⋊ C2 |
| Hall | C72×C13 ⋊ C3×D3 |
| Hall | C3×#3862 ⋊ D13 |
| Sylow | C72 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3⋊#64422 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7^2,13|c^a=c^2,d^a=d^6,f^a=f^12,d^b=d^2,e^b=e^4378 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C3⋊#64422, D39×#64422, D3×#16838466, … |
| maximal normal subgroup of | D13×C3⋊#64422, D39×#64422, D3×#16838466, … |
| maximal quotient of | C3⋊#21439542, C2×C3⋊#16838466 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 312);