Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C8 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×C3⋊C8 |
| unambiguous semidirect product | C3⋊(C3×C52×C8) |
| derived | C3 ⋊ C3×C52×C8 |
| Hall | C32×C52 ⋊ C8 |
| Sylow | C32 ⋊ C52×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C52 | D3 |
| commutator, hypocenter | C3 | C3×C52×C8 |
| Frattini | C4 | C3×C52×D3 |
| Fitting | C32×C4×C52 | C2 |
| socle, prime radical | C2×C32×C52 | C4 |
| cosocle | C3×C4 | C2×C3×C52 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C4×C52 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 263);