Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of C3⋊#1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#6033 |
| unambiguous semidirect product | C3⋊(C3×#6033) |
| derived | C3×C52 ⋊ C3×C8 |
| Hall | C32×C52 ⋊ C8 |
| Sylow | C52 ⋊ C3×C3⋊C8 |
| Sylow | C32 ⋊ #6033 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊#1043 |
| commutator, hypocenter | C3×C52 | C3×C8 |
| Frattini | C2 | C3×C3⋊#1043 |
| Fitting, socle, prime radical | C2×C32×C52 | C4 |
| cosocle | C3×#1039 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 395);