Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×D11×C25 |
| Fitting, Hall | C3×C112×C25 ⋊ C2 |
| derived | C11 ⋊ C2×C3×C11×C25 |
| Hall | C112×C25 ⋊ C2×C3 |
| Hall | C3×C112 ⋊ C2×C25 |
| Sylow | C112 ⋊ C2×C3×C25 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
5775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D112×C25, C3×C11×D11×D25, C3×D11×D275, … |
| maximal normal subgroup of | C3×D112×C25, C3×C11×D11×D25, C3×D11×D275, … |
| maximal quotient of | C3×C11×C25×Dic11, C2×C3×C11×D11×C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 79);