Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×C3⋊C8 |
| unambiguous semidirect product | C3⋊(C3×C8×C17) |
| derived | C3 ⋊ C3×C8×C17 |
| Hall | C32×C17 ⋊ C8 |
| Sylow | C32 ⋊ C8×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C17 | D3 |
| commutator, hypocenter | C3 | C3×C8×C17 |
| Frattini | C4 | C3×D3×C17 |
| Fitting | C32×C4×C17 | C2 |
| socle, prime radical | C2×C32×C17 | C4 |
| cosocle | C3×C4 | C2×C3×C17 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C4×C17 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 408 |
612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 34);