Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D15 |
| unambiguous semidirect product | C3⋊(C32×C5×D5) |
| unambiguous semidirect product | C5⋊(C32×C5×D3) |
| Fitting, socle, Hall | C33×C52 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C32×C5 |
| Sylow | C33 ⋊ C5×D5 |
| Sylow | C52 ⋊ C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C33×C52 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C32×C5 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D15⋊D5, C3×C5×(C3⋊D3)⋊D5, C3×D152, … |
| maximal normal subgroup of | C32×D15⋊D5, C3×C5×(C3⋊D3)⋊D5, C3×D152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 104);