Finite Group DatabasebetaFinite Group Databasebeta| order | 8570 |
| automorphism | Aut(G) order 14671840 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4285 |
| unambiguous semidirect product | C5⋊D857 |
| unambiguous semidirect product | C857⋊D5 |
| Fitting, socle, derived, Hall | C5×C857 ⋊ C2 |
| Sylow | C857 ⋊ D5 |
| Sylow | C5 ⋊ D857 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C857 | C2 |
| LCS | G ▷ C5×C857 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,857|b^a=b^4,c^a=c^8562144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30686213, #30686214, D5×D857, … |
| maximal normal subgroup of | #30686213, #30686214, D5×D857, … |
| maximal quotient of | Dic4285, C2×D4285, C3×D4285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8570, 3);