Finite Group DatabasebetaFinite Group Databasebeta| order | 6030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D603 |
| unambiguous semidirect product | C9⋊(C5×D67) |
| unambiguous semidirect product | C67⋊(C5×D9) |
| Fitting, Hall | C5×C9×C67 ⋊ C2 |
| derived, Hall | C9×C67 ⋊ C2×C5 |
| Hall | C5×C67 ⋊ D9 |
| Sylow | C67 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ D67 |
| Sylow | C9 ⋊ C5×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D603 |
| commutator, hypocenter | C9×C67 | C2×C5 |
| Frattini | C3 | C5×D201 |
| Fitting | C5×C9×C67 | C2 |
| socle | C3×C5×C67 | D3 |
| LCS | G ▷ C9×C67 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
1515 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D67, D5×D603, D45⋊D67, … |
| maximal normal subgroup of | C5×D9×D67, D5×D603, D45⋊D67, … |
| maximal quotient of | C5×Dic603, C2×C5×D603, C25×D603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6030, 7);