Finite Group DatabasebetaFinite Group Databasebeta| order | 12006 |
| isoclinism | isoclinic class of C3⋊D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C3 |
| direct product | C29×C3⋊D69 |
| unambiguous semidirect product | C3⋊(C29×D69) |
| unambiguous semidirect product | C23⋊(C3⋊D3×C29) |
| Fitting, socle, Hall | C32×C23×C29 ⋊ C2 |
| derived, Hall | C32×C23 ⋊ C2×C29 |
| Hall | C23×C29 ⋊ C3⋊D3 |
| Hall | C32×C29 ⋊ D23 |
| Sylow | C23 ⋊ C3⋊D3×C29 |
| Sylow | C32 ⋊ C29×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊D69 |
| commutator, cosocle, hypocenter | C32×C23 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C29 | C2 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C29 | |
48 conjugacy classes of subgroups.
3045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C29×D69, D87⋊D69, D29×C3⋊D69, … |
| maximal normal subgroup of | D3×C29×D69, D87⋊D69, D29×C3⋊D69, … |
| maximal quotient of | C29×C3⋊Dic69, C2×C29×C3⋊D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12006, 11);