Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| automorphism | Aut(G) order 12644424 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4503 |
| unambiguous semidirect product | C3⋊D1501 |
| unambiguous semidirect product | C19⋊D237 |
| unambiguous semidirect product | C79⋊D57 |
| Fitting, socle, derived, Hall | C3×C19×C79 ⋊ C2 |
| Hall | C19×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ D19 |
| Sylow | C79 ⋊ D57 |
| Hall | C3×C19 ⋊ D79 |
| Sylow | C19 ⋊ D237 |
| Sylow | C3 ⋊ D1501 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C79 | C2 |
| LCS | G ▷ C3×C19×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,79|b^a=b^2,c^a=c^18,d^a=d^782253 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D57×D79, D19×D237, D3×D1501, … |
| maximal normal subgroup of | D57×D79, D19×D237, D3×D1501, … |
| maximal quotient of | Dic4503, C2×D4503, D13509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 12);