Finite Group DatabasebetaFinite Group Databasebeta| order | 5406 |
| automorphism | Aut(G) order 4497792 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2703 |
| unambiguous semidirect product | C3⋊D901 |
| unambiguous semidirect product | C17⋊D159 |
| unambiguous semidirect product | C53⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C53 ⋊ C2 |
| Hall | C17×C53 ⋊ D3 |
| Hall | C3×C53 ⋊ D17 |
| Sylow | C53 ⋊ D51 |
| Hall | C3×C17 ⋊ D53 |
| Sylow | C17 ⋊ D159 |
| Sylow | C3 ⋊ D901 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C53 | C2 |
| LCS | G ▷ C3×C17×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,53|b^a=b^2,c^a=c^16,d^a=d^521353 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D53, D17×D159, D3×D901, … |
| maximal normal subgroup of | D51×D53, D17×D159, D3×D901, … |
| maximal quotient of | Dic2703, C2×D2703, D8109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5406, 8);