Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×ΓL(1,𝔽16) |
| unambiguous semidirect product | (C2×C3)⋊(C11×AGL(1,𝔽5)) |
| unambiguous semidirect product | D5⋊(C11×Dic3) |
| Fitting, socle | C2×C3×C5×C11 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C2×C4×C11 |
| Hall | C3×C5×C11 ⋊ C2×C4 |
| Hall | C5×C11 ⋊ C2×Dic3 |
| Hall | C3×C11 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C11×Dic3 |
| Sylow | C3 ⋊ C2×C11×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C2×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C4 |
| prime radical | C2×C3×D5×C11 | C2 |
| cosocle | C3×D5 | C22×C11 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C11 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 164);