Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×C13×D7) |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C32×C13 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C13×C7⋊D7 ⋊ C32 |
| Hall | C72×C13 ⋊ C2×C32 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×C13 |
| Hall | C7⋊D7 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C13 | |
112 conjugacy classes of subgroups.
858 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 254);