Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C22×C17×D9 |
| unambiguous semidirect product | C9⋊(C23×C17) |
| unambiguous semidirect product | (C2×C9)⋊(C22×C17) |
| Fitting | C22×C9×C17 ⋊ C2 |
| derived, Sylow | C9 ⋊ C23×C17 |
| Hall | C9×C17 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C17 | D9 |
| commutator, cosocle, hypocenter | C9 | C23×C17 |
| Frattini | C3 | C22×D3×C17 |
| Fitting | C22×C9×C17 | C2 |
| socle | C22×C3×C17 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C17 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 612 |
408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 50);