Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D79 |
| Fitting, socle, derived, Hall | C19×C79 ⋊ C2×C3 |
| Hall | C19⋊C3×C79 ⋊ C2 |
| Hall | D1501 ⋊ C3 |
| Sylow | C79 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D79 |
| Sylow | C19 ⋊ C3×D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C79 | C2×C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,79|c^a=c^18,d^a=d^78,c^b=c^7360 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D79, C2×(C19⋊C3)⋊D79, #41028277, … |
| maximal normal subgroup of | D19⋊C3×D79, C2×(C19⋊C3)⋊D79, #41028277, … |
| maximal quotient of | (C19⋊C3)⋊Dic79, C2×(C19⋊C3)⋊D79, #4294⋊D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 22);