Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C361 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C361 |
| unambiguous semidirect product | C3⋊(C2×C5×C361) |
| Fitting, Hall | C3×C5×C361 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C361 |
| Hall | C3×C361 ⋊ C2×C5 |
| Hall | C3×C5 ⋊ C2×C361 |
24 conjugacy classes of subgroups.
5415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D361, D3×D5×C361, D3×D1805, … |
| maximal normal subgroup of | C5×D3×D361, D3×D5×C361, D3×D1805, … |
| maximal quotient of | C5×Dic3×C361, C2×C5×D3×C361, C5×D9×C361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 9);