Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | Dic3×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×Dic3) |
| unambiguous semidirect product | (Dic3×D11)⋊C5 |
| unambiguous semidirect product | (C3×AGL(1,𝔽11))⋊C4 |
| derived, Hall | C3×C11 ⋊ C2×C4×C5 |
| Hall | Dic3×D11 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×C4 |
| Hall | C11⋊C5 ⋊ C2×Dic3 |
| Sylow | C11 ⋊ C2×C5×Dic3 |
| Sylow | C3 ⋊ C4×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×AGL(1,𝔽11) |
| commutator, hypocenter | C3×C11 | C2×C4×C5 |
| Fitting, socle, cosocle | C2×C3×C11 | C22×C5 |
| prime radical | C2×C3×AGL(1,𝔽11) | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 15);