Finite Group DatabasebetaFinite Group Databasebeta| order | 30150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1675 |
| unambiguous semidirect product | C25⋊(C32×D67) |
| Fitting, Hall | C32×C25×C67 ⋊ C2 |
| derived, Hall | C25×C67 ⋊ C2×C32 |
| Hall | C32×C67 ⋊ D25 |
| Hall | C32×C25 ⋊ D67 |
| Sylow | C67 ⋊ C32×D25 |
| Sylow | C25 ⋊ C32×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1675 |
| commutator, cosocle, hypocenter | C25×C67 | C2×C32 |
| Frattini | C5 | C32×D335 |
| Fitting | C32×C25×C67 | C2 |
| socle | C32×C5×C67 | D5 |
| LCS | G ▷ C25×C67 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15075 |
7551 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30150, 24);