Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C8×C11⋊C5 |
| unambiguous semidirect product | (C8×C11)⋊(C3×C5) |
| unambiguous semidirect product | (C3×C8×C11)⋊C5 |
| Fitting, Hall | C3×C8×C11 ⋊ C5 |
| derived, Sylow | C11 ⋊ C3×C5×C8 |
| Hall | C8×C11 ⋊ C3×C5 |
| Hall | C3×C11 ⋊ C5×C8 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C8×AGL(1,𝔽11), D3×C8×C11⋊C5, C8×C3⋊AGL(1,𝔽11), … |
| maximal normal subgroup of | C3×C8×AGL(1,𝔽11), D3×C8×C11⋊C5, C8×C3⋊AGL(1,𝔽11), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 4);