Finite Group DatabasebetaFinite Group Databasebeta| order | 8170 |
| automorphism | Aut(G) order 12353040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4085 |
| unambiguous semidirect product | C5⋊D817 |
| unambiguous semidirect product | C19⋊D215 |
| unambiguous semidirect product | C43⋊D95 |
| Fitting, socle, derived, Hall | C5×C19×C43 ⋊ C2 |
| Hall | C19×C43 ⋊ D5 |
| Hall | C5×C43 ⋊ D19 |
| Hall | C5×C19 ⋊ D43 |
| Sylow | C43 ⋊ D95 |
| Sylow | C19 ⋊ D215 |
| Sylow | C5 ⋊ D817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C43 | C2 |
| LCS | G ▷ C5×C19×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,19,43|b^a=b^4,c^a=c^18,d^a=d^422044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D95, D19×D215, D5×D817, … |
| maximal normal subgroup of | D43×D95, D19×D215, D5×D817, … |
| maximal quotient of | Dic4085, C2×D4085, C3×D4085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8170, 8);