Finite Group DatabasebetaFinite Group Databasebeta| order | 12078 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2013 |
| unambiguous semidirect product | C3⋊(C3×D671) |
| unambiguous semidirect product | C11⋊(C3×D183) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C2 |
| derived | C3×C11×C61 ⋊ C2×C3 |
| Hall | C11×C61 ⋊ C3×D3 |
| Hall | C32×C61 ⋊ D11 |
| Hall | C32×C11 ⋊ D61 |
| Sylow | C61 ⋊ C3×D33 |
| Sylow | C11 ⋊ C3×D183 |
| Sylow | C32 ⋊ D671 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2013 |
| commutator, cosocle, hypocenter | C3×C11×C61 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C2 |
| LCS | G ▷ C3×C11×C61 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
3024 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D33×D61, C3×D11×D183, C3×D3×D671, … |
| maximal normal subgroup of | C3×D33×D61, C3×D11×D183, C3×D3×D671, … |
| maximal quotient of | C3×Dic2013, C2×C3×D2013 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12078, 26);