Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×Dic17 |
| derived, Sylow | C17 ⋊ C2×C4×C9 |
| Hall | C9×C17 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C9 | D17 |
| commutator, hypocenter | C17 | C2×C4×C9 |
| Frattini | C2×C3 | C2×C3×D17 |
| Fitting | C22×C9×C17 | C2 |
| socle, prime radical | C22×C3×C17 | C2×C3 |
| cosocle | C2×C3×C17 | C22×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C9 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1224 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 18);