Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×AGL(1,𝔽5) |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊(C2×C11) |
| unambiguous semidirect product | ΓL(1,𝔽16)⋊(C2×C11) |
| Fitting, socle, Hall | C3×C5×C11 ⋊ C2×C4 |
| derived, Hall | C3×C5 ⋊ C2×C4×C11 |
| Hall | C5×C11 ⋊ C4×D3 |
| Hall | C3×C11 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D3×C11 |
| Sylow | C3 ⋊ C2×C11×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C2×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11 | C2×C4 |
| prime radical | D3×D5×C11 | C2 |
| cosocle | C3×D5 | C22×C11 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C11 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×D11, D3×AGL(1,𝔽5)×C11⋊C5 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×D11, D3×AGL(1,𝔽5)×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 149);