Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D3×#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#595 |
| unambiguous semidirect product | (C3×#595)⋊(C2×C3) |
| unambiguous semidirect product | (C3⋊#595)⋊(C2×C3) |
| Fitting, socle, Hall | C32×C17 ⋊ C2×C4 |
| derived | C3×C17 ⋊ C2×C3×C4 |
| Sylow | C17 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C2×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×#595 |
| commutator, hypocenter | C3×C17 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17 | C2×C4 |
| prime radical | C3×D3×D17 | C2 |
| cosocle | C3×D17 | C22×C3 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3 | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 102 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#3633, D32×#595, D3×C3⋊#3633, … |
| maximal normal subgroup of | C3×D3×#3633, D32×#595, D3×C3⋊#3633 |
| maximal quotient of | AGL(1,ℤ/9)×#595, D3×A4×#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 128);