Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | D33×C11⋊C25 |
| unambiguous semidirect product | C3⋊(D11×C11⋊C25) |
| derived, Hall | C3×C112 ⋊ C2×C25 |
| Hall | C3×C11×C11⋊C25 ⋊ C2 |
| Hall | C11×C11⋊C25 ⋊ D3 |
| Hall | C11×D33 ⋊ C25 |
| Sylow | C112 ⋊ D3×C25 |
| Sylow | C3 ⋊ D11×C11⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C11⋊C5×D33 |
| commutator, hypocenter | C3×C112 | C2×C25 |
| Fitting, socle, cosocle | C3×C5×C112 | C2×C5 |
| prime radical | C5×C11×D33 | C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D11⋊C25, (C3⋊(D11⋊C25))⋊D11, D3×D11×C11⋊C25, … |
| maximal normal subgroup of | D33×D11⋊C25, (C3⋊(D11⋊C25))⋊D11, D3×D11×C11⋊C25, … |
| maximal quotient of | Dic33×C11⋊C25, C2×D33×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 67);