Finite Group DatabasebetaFinite Group Databasebeta| order | 12084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊C3×D53 |
| unambiguous semidirect product | C53⋊(C22×C19⋊C3) |
| unambiguous semidirect product | (C2×C53)⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C2×C19×D53)⋊C3 |
| Fitting, socle | C2×C19×C53 ⋊ C2×C3 |
| derived, Hall | C19×C53 ⋊ C22×C3 |
| Hall | C2×C19×D53 ⋊ C3 |
| Hall | C53×C19⋊C3 ⋊ C22 |
| Sylow | C53 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C2×C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊C3×D53 |
| commutator, cosocle, hypocenter | C19×C53 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C53 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
504 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D53×#4296, D3×C19⋊C3×D53, C2×C3×C19⋊C3×D53, … |
| maximal normal subgroup of | C2×D53×#4296, C2×C3×C19⋊C3×D53 |
| maximal quotient of | C2×D53×#4294, D3×C19⋊C3×D53, C2×C3×C19⋊C3×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12084, 19);