Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #338⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×#338⋊C3 |
| unambiguous semidirect product | (C2×#338)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#338)⋊C3 |
| Fitting, Hall | C2×C5×#338 ⋊ C3 |
| derived | #338 ⋊ C2×C3×C5 |
| Sylow | C2×#338 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C5 | C42⋊C3 |
| commutator, cosocle, hypocenter | #338 | C2×C3×C5 |
| Frattini | C22×C4 | C2×C5×A4 |
| Fitting | C2×C5×#338 | C3 |
| socle | C22×C5 | #95⋊C3 |
| LCS | G ▷ #338 | |
| UCS | C1 ◁ C2×C4×C5 | |
184 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236379);