Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)⋊D91) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D273 |
| Fitting, socle, derived | C3×C72×C13 ⋊ C2×C3 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C72×C13 ⋊ C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ D13 |
| Sylow | C72 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3⋊(ΓL(1,𝔽8)⋊D7) |
| 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 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7^2,13|c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^12,d^b=d^2687 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 318);