Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112×C25 · Schur multiplier (H2) = C11 |
| direct product | D3×C112×C25 |
| unambiguous semidirect product | C3⋊(C2×C112×C25) |
| Fitting, Hall | C3×C112×C25 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C112×C25 |
| Hall | C3×C112 ⋊ C2×C25 |
| Hall | C3×C25 ⋊ C2×C112 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
9075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D11×C25, D3×C25×C11⋊D11, D3×C112×D25, … |
| maximal normal subgroup of | D3×C11×D11×C25, D3×C25×C11⋊D11, D3×C112×D25, … |
| maximal quotient of | C112×Dic3×C25, C2×D3×C112×C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 84);