Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | D3×C7×#63270 |
| unambiguous semidirect product | C3⋊(C2×C7×#63270) |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived | C3×C7×C13 ⋊ C2×C3×C7 |
| Hall | C3×C7×#63270 ⋊ C2 |
| Hall | C72×C13 ⋊ C3×D3 |
| Sylow | C72 ⋊ D3×C13⋊C3 |
| Sylow | C13 ⋊ D3×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×#63270 |
| commutator, cosocle, hypocenter | C3×C7×C13 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
693 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C7×#10587716, D3×C7×#10587722, D3×C7×#10587720, … |
| maximal normal subgroup of | D3×C7×#10587716, D3×C7×#10587722, D3×C7×#10587720, … |
| maximal quotient of | C7×Dic3×#63270, C2×D3×C7×#63270 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 286);