Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16838413 |
| Fitting, derived | C3×C13×C49 ⋊ C2×C3 |
| Hall | C3×#14274254 ⋊ C2 |
| Hall | C13×C49 ⋊ C3×D3 |
| Sylow | C49 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ D3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C13×C49 | C2×C3 |
| Frattini | C7 | C3⋊#10587716 |
| socle | C3×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,13,7|d^7=f^2,c^a=c^2,e^a=e^12,d^b=d^2f,e^b=e^3,f^b=f^2351 conjugacy classes — view the full character table.
| maximal subgroup of | #16838417⋊D3, #16838419⋊D3, D3×#16838413, … |
| maximal normal subgroup of | #16838417⋊D3, #16838419⋊D3, D3×#16838413, … |
| maximal quotient of | C3⋊#21439437, C2×C3⋊#16838413 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 51);