Finite Group DatabasebetaFinite Group Databasebeta| order | 12084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D159 |
| unambiguous semidirect product | (C3×D19)⋊D53 |
| unambiguous semidirect product | (D19×C53)⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C53 ⋊ C22 |
| Hall | C19×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D53 |
| Sylow | C53 ⋊ D3×D19 |
| Sylow | C19 ⋊ C2×D159 |
| Sylow | C3 ⋊ D19×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C53 | C22 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
891 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D477, D19⋊C3×D159, C3×D19×D159, … |
| maximal normal subgroup of | D19⋊C3×D159, C3×D19×D159 |
| maximal quotient of | D19×D477, C3×D19×D159, D57×D159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12084, 28);