Finite Group DatabasebetaFinite Group Databasebeta| order | 12006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D261 |
| unambiguous semidirect product | C9⋊(C23×D29) |
| unambiguous semidirect product | C29⋊(D9×C23) |
| Fitting, Hall | C9×C23×C29 ⋊ C2 |
| derived, Hall | C9×C29 ⋊ C2×C23 |
| Hall | C23×C29 ⋊ D9 |
| Hall | C9×C23 ⋊ D29 |
| Sylow | C29 ⋊ D9×C23 |
| Sylow | C9 ⋊ C23×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D261 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C23 |
| Frattini | C3 | C23×D87 |
| Fitting | C9×C23×C29 | C2 |
| socle | C3×C23×C29 | D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
3036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C23×D29, D23×D261, D207⋊D29, … |
| maximal normal subgroup of | D9×C23×D29, D23×D261, D207⋊D29, … |
| maximal quotient of | C23×Dic261, C2×C23×D261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12006, 6);