Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C11⋊C5×D33 |
| unambiguous semidirect product | C3⋊(C5×D11×C11⋊C5) |
| Fitting, socle | C3×C5×C112 ⋊ C2×C5 |
| derived, Hall | C3×C112 ⋊ C2×C52 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C2 |
| Hall | C5×C11×C11⋊C5 ⋊ D3 |
| Hall | C11×D33 ⋊ C52 |
| Sylow | C112 ⋊ C52×D3 |
| Sylow | C3 ⋊ C5×D11×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊C5×D33 |
| commutator, cosocle, hypocenter | C3×C112 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C2×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
630 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 144);