Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D9×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D9×D17 |
| unambiguous semidirect product | (C17×D9)⋊C22 |
| unambiguous semidirect product | (C9×D17)⋊C22 |
| unambiguous semidirect product | D153⋊C22 |
| Fitting | C2×C9×C17 ⋊ C22 |
| derived, Hall | C9×C17 ⋊ C23 |
| Sylow | C17 ⋊ C22×D9 |
| Sylow | C9 ⋊ C22×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×D17 |
| commutator, cosocle, hypocenter | C9×C17 | C23 |
| Frattini | C3 | C2×D3×D17 |
| Fitting | C2×C9×C17 | C22 |
| socle | C2×C3×C17 | C2×D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 306 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 47);