Finite Group DatabasebetaFinite Group Databasebeta| order | 30150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5025 |
| unambiguous semidirect product | C25⋊(C3⋊D201) |
| unambiguous semidirect product | C67⋊(C3⋊D75) |
| Fitting, derived, Hall | C32×C25×C67 ⋊ C2 |
| Hall | C25×C67 ⋊ C3⋊D3 |
| Hall | C32×C67 ⋊ D25 |
| Hall | C32×C25 ⋊ D67 |
| Sylow | C67 ⋊ C3⋊D75 |
| Sylow | C25 ⋊ C3⋊D201 |
| Sylow | C32 ⋊ D1675 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C25×C67 | C2 |
| Frattini | C5 | C3⋊D1005 |
| socle | C32×C5×C67 | D5 |
| LCS | G ▷ C32×C25×C67 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15075 |
Polycyclic presentation:
2,3^2,5,67,5|d^5=f^4,b^a=b^2,c^a=c^2,d^a=d^4f,e^a=e^66,f^a=f^47539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30150, 32);