Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#20258405 |
| derived, Sylow | C112 ⋊ C2×C3×C25 |
| Hall | C3×#15690027 ⋊ C2 |
| Hall | #15690027 ⋊ C2×C3 |
| Hall | C3×C11×D11 ⋊ C25 |
| Hall | C3×C112 ⋊ C2×C25 |
| Hall | C11×D11 ⋊ C3×C25 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20258402⋊C2, #20258405⋊D3, D3×#20258405, … |
| maximal normal subgroup of | C3×#20258402⋊C2, #20258405⋊D3, D3×#20258405, … |
| maximal quotient of | C3×#27130779, C2×C3×#20258405 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 47);