Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C23×C25 |
| unambiguous semidirect product | C3⋊(C2×C3×C23×C25) |
| Fitting, Hall | C32×C23×C25 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C23×C25 |
| Hall | C32×C25 ⋊ C2×C23 |
| Hall | C32×C23 ⋊ C2×C25 |
| Sylow | C32 ⋊ C2×C23×C25 |
54 conjugacy classes of subgroups.
5175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C25×D23, C3×D3×C23×D25, C3×D3×D575, … |
| maximal normal subgroup of | C3×D3×C25×D23, C3×D3×C23×D25, C3×D3×D575, … |
| maximal quotient of | C3×Dic3×C23×C25, C2×C3×D3×C23×C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 13);