Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C11×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C3×C5×C11 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C4×C11 |
| Hall | C5×C11 ⋊ Dic3 |
| Hall | C3×C11 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11×Dic3 |
| Sylow | C3 ⋊ C11×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11 | C4 |
| prime radical | C3×D5×C11 | C2 |
| cosocle | C3×D5 | C2×C11 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 165 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 23);