Finite Group DatabasebetaFinite Group Databasebeta| order | 5370 |
| automorphism | Aut(G) order 3823440 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2685 |
| unambiguous semidirect product | C3⋊D895 |
| unambiguous semidirect product | C5⋊D537 |
| unambiguous semidirect product | C179⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C179 ⋊ C2 |
| Hall | C5×C179 ⋊ D3 |
| Hall | C3×C179 ⋊ D5 |
| Sylow | C179 ⋊ D15 |
| Hall | C3×C5 ⋊ D179 |
| Sylow | C5 ⋊ D537 |
| Sylow | C3 ⋊ D895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C179 | C2 |
| LCS | G ▷ C3×C5×C179 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,179|b^a=b^2,c^a=c^4,d^a=d^1781344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8055, C3⋊D2685, C3×D2685, … |
| maximal normal subgroup of | C3×D2685, C5×D2685, C7×D2685 |
| maximal quotient of | D8055, C3⋊D2685, C3×D2685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5370, 8);