Finite Group DatabasebetaFinite Group Databasebeta| order | 5190 |
| automorphism | Aut(G) order 3570720 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2595 |
| unambiguous semidirect product | C3⋊D865 |
| unambiguous semidirect product | C5⋊D519 |
| unambiguous semidirect product | C173⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C173 ⋊ C2 |
| Hall | C5×C173 ⋊ D3 |
| Hall | C3×C173 ⋊ D5 |
| Sylow | C173 ⋊ D15 |
| Hall | C3×C5 ⋊ D173 |
| Sylow | C5 ⋊ D519 |
| Sylow | C3 ⋊ D865 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C173 | C2 |
| LCS | G ▷ C3×C5×C173 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,173|b^a=b^2,c^a=c^4,d^a=d^1721299 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7785, C3⋊D2595, C3×D2595, … |
| maximal normal subgroup of | C3×D2595, C5×D2595, C7×D2595 |
| maximal quotient of | D7785, C3⋊D2595, C3×D2595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5190, 8);