Finite Group DatabasebetaFinite Group Databasebeta| order | 4770 |
| automorphism | Aut(G) order 2976480 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2385 |
| unambiguous semidirect product | C5⋊D477 |
| unambiguous semidirect product | C9⋊D265 |
| unambiguous semidirect product | C53⋊D45 |
| Fitting, derived, Hall | C5×C9×C53 ⋊ C2 |
| Hall | C9×C53 ⋊ D5 |
| Hall | C5×C53 ⋊ D9 |
| Sylow | C53 ⋊ D45 |
| Hall | C5×C9 ⋊ D53 |
| Sylow | C9 ⋊ D265 |
| Sylow | C5 ⋊ D477 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C53 | C2 |
| Frattini | C3 | D795 |
| socle | C3×C5×C53 | D3 |
| LCS | G ▷ C5×C9×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2385 |
Polycyclic presentation:
2,3,5,53,3|b^3=e^2,b^a=b^2e,c^a=c^4,d^a=d^52,e^a=e^21194 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11925, C5×D2385, C5⋊D2385, … |
| maximal normal subgroup of | C5×D2385, C7×D2385 |
| maximal quotient of | D11925, C5×D2385, C5⋊D2385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4770, 8);