Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×Q8×C11⋊C5 |
| unambiguous semidirect product | (C3×Q8×C11)⋊C5 |
| Fitting, Hall | C3×Q8×C11 ⋊ C5 |
| Hall | Q8×C11 ⋊ C3×C5 |
| Hall | C3×C11 ⋊ C5×Q8 |
| Sylow | C11 ⋊ C3×C5×Q8 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | C3×SD16×C11⋊C5, C3×#4325⋊C5, #215×C11⋊C5, … |
| maximal normal subgroup of | C3×SD16×C11⋊C5, C3×#4325⋊C5, #215×C11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 40);