Finite Group DatabasebetaFinite Group Databasebeta| order | 5142 |
| automorphism | Aut(G) order 4401552 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2571 |
| unambiguous semidirect product | C3⋊D857 |
| unambiguous semidirect product | C857⋊D3 |
| Fitting, socle, derived, Hall | C3×C857 ⋊ C2 |
| Sylow | C857 ⋊ D3 |
| Sylow | C3 ⋊ D857 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C857 | C2 |
| LCS | G ▷ C3×C857 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,857|b^a=b^2,c^a=c^8561287 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7713, C3⋊D2571, C3×D2571, … |
| maximal normal subgroup of | C3×D2571, C5×D2571, C7×D2571 |
| maximal quotient of | D7713, C3⋊D2571, C3×D2571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5142, 3);