Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | D3×C7×C13×ΓL(1,𝔽8) |
| unambiguous semidirect product | C3⋊(C2×C7×C13×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (D3×C7)⋊(C3×C7×C13) |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived | C3×C7 ⋊ C2×C3×C7×C13 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C72×C13 ⋊ C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×C13 |
| Sylow | C72 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | D3×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C3×C7 | C2×C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C7×C13 | |
88 conjugacy classes of subgroups.
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 283);