Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊#4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊#4380 |
| unambiguous semidirect product | C3⋊(C3×#4380) |
| Fitting, socle, Hall | C34×C5 ⋊ C4 |
| derived | C33×C5 ⋊ C3×C4 |
| Sylow | C34 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×C3⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#4380 |
| commutator, hypocenter | C33×C5 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C4 |
| prime radical | C32×C3⋊D15 | C2 |
| cosocle | C3×C3⋊D15 | C2×C3 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C3 | |
192 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 436);