Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C11 |
| direct product | C3×#20258403 |
| derived, Sylow | C112 ⋊ C2×C3×C25 |
| Hall | C3×#15690029 ⋊ C2 |
| Hall | #15690029 ⋊ C2×C3 |
| Hall | C3×C11⋊D11 ⋊ C25 |
| Hall | C3×C112 ⋊ C2×C25 |
| Hall | C11⋊D11 ⋊ C3×C25 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20258406⋊C2, C3×#20258400⋊C2, C3×#27130800, … |
| maximal normal subgroup of | C3×#20258406⋊C2, C3×#20258400⋊C2, C3×#27130800, … |
| maximal quotient of | C3×#27130777, C2×C3×#20258403 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 45);