Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of C3⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#3624 |
| unambiguous semidirect product | C3⋊(C3×#3624) |
| derived | C3×C17 ⋊ C3×C8 |
| Hall | C32×C17 ⋊ C8 |
| Sylow | C17 ⋊ C3×C3⋊C8 |
| Sylow | C32 ⋊ #3624 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊#595 |
| commutator, hypocenter | C3×C17 | C3×C8 |
| Frattini | C2 | C3×C3⋊#595 |
| Fitting, socle, prime radical | C2×C32×C17 | C4 |
| cosocle | C3×Dic17 | C2×C3 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C3 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 408 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 54);