Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊#64422 |
| unambiguous semidirect product | C3⋊(C13×#64422) |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C2×C3×C13 |
| Hall | C3×C13×#3862 ⋊ C2 |
| Hall | C72×C13 ⋊ C3×D3 |
| Hall | C3×#3862 ⋊ C2×C13 |
| Sylow | C72 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊#64422 |
| commutator, cosocle, hypocenter | C3×C72 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C13 | |
76 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C3⋊#64422, D3×C13×#64422, #37525344, … |
| maximal normal subgroup of | D13×C3⋊#64422, D3×C13×#64422, #37525344, … |
| maximal quotient of | C13×C3⋊#10596872, C2×C13×C3⋊#64422 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 307);