Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of C3⋊D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊D75 |
| unambiguous semidirect product | C3⋊(C3×D75) |
| unambiguous semidirect product | C25⋊(C3×C3⋊D3) |
| Fitting, Hall | C33×C25 ⋊ C2 |
| derived | C32×C25 ⋊ C2×C3 |
| Sylow | C33 ⋊ D25 |
| Sylow | C25 ⋊ C3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C2×C3 |
| Frattini | C5 | C3×C3⋊D15 |
| Fitting | C33×C25 | C2 |
| socle | C33×C5 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 450 |
342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 36);