Finite Group DatabasebetaFinite Group Databasebeta| order | 7470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D415 |
| unambiguous semidirect product | C5⋊(C9×D83) |
| unambiguous semidirect product | C83⋊(C9×D5) |
| Fitting, Hall | C5×C9×C83 ⋊ C2 |
| derived, Hall | C5×C83 ⋊ C2×C9 |
| Hall | C9×C83 ⋊ D5 |
| Sylow | C83 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D83 |
| Sylow | C5 ⋊ C9×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D415 |
| commutator, hypocenter | C5×C83 | C2×C9 |
| Frattini | C3 | C3×D415 |
| Fitting | C5×C9×C83 | C2 |
| socle | C3×C5×C83 | C2×C3 |
| LCS | G ▷ C5×C83 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
1881 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D83, D9×D415, D45⋊D83, … |
| maximal normal subgroup of | C9×D5×D83, D9×D415, D45⋊D83, … |
| maximal quotient of | C9×Dic415, C2×C9×D415, C9×D2075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7470, 4);