Finite Group DatabasebetaFinite Group Databasebeta| order | 7470 |
| automorphism | Aut(G) order 7350480 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3735 |
| unambiguous semidirect product | C5⋊D747 |
| unambiguous semidirect product | C9⋊D415 |
| unambiguous semidirect product | C83⋊D45 |
| Fitting, derived, Hall | C5×C9×C83 ⋊ C2 |
| Hall | C9×C83 ⋊ D5 |
| Hall | C5×C83 ⋊ D9 |
| Sylow | C83 ⋊ D45 |
| Hall | C5×C9 ⋊ D83 |
| Sylow | C9 ⋊ D415 |
| Sylow | C5 ⋊ D747 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C83 | C2 |
| Frattini | C3 | D1245 |
| socle | C3×C5×C83 | D3 |
| LCS | G ▷ C5×C9×C83 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,83,3|b^3=e^2,b^a=b^2e,c^a=c^4,d^a=d^82,e^a=e^21869 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×D83, D5×D747, D9×D415, … |
| maximal normal subgroup of | D45×D83, D5×D747, D9×D415, … |
| maximal quotient of | Dic3735, C2×D3735, D18675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7470, 8);