Finite Group DatabasebetaFinite Group Databasebeta| order | 12054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2009 |
| unambiguous semidirect product | C41⋊(C3×D49) |
| Fitting, Hall | C3×C41×C49 ⋊ C2 |
| derived, Hall | C41×C49 ⋊ C2×C3 |
| Hall | C3×C49 ⋊ D41 |
| Hall | C3×C41 ⋊ D49 |
| Sylow | C49 ⋊ C3×D41 |
| Sylow | C41 ⋊ C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2009 |
| commutator, cosocle, hypocenter | C41×C49 | C2×C3 |
| Frattini | C7 | C3×D287 |
| Fitting | C3×C41×C49 | C2 |
| socle | C3×C7×C41 | D7 |
| LCS | G ▷ C41×C49 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
3018 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D41×D49, D3×D2009, D123⋊D49, … |
| maximal normal subgroup of | C3×D41×D49, D3×D2009, D123⋊D49, … |
| maximal quotient of | C3×Dic2009, C2×C3×D2009, C9×D2009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12054, 8);