Finite Group DatabasebetaFinite Group Databasebeta| order | 12078 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D183 |
| unambiguous semidirect product | C3⋊(C11×D183) |
| unambiguous semidirect product | C61⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C2 |
| derived, Hall | C32×C61 ⋊ C2×C11 |
| Hall | C11×C61 ⋊ C3⋊D3 |
| Hall | C32×C11 ⋊ D61 |
| Sylow | C61 ⋊ C11×C3⋊D3 |
| Sylow | C32 ⋊ C11×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D183 |
| commutator, cosocle, hypocenter | C32×C61 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C2 |
| LCS | G ▷ C32×C61 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
3036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#14555574, C11⋊#14555574, D3×C11×D183, … |
| maximal normal subgroup of | C11×#14555574, C11⋊#14555574, D3×C11×D183, … |
| maximal quotient of | C11×C3⋊Dic183, C2×C11×C3⋊D183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12078, 24);