Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#3531⋊C5 |
| unambiguous semidirect product | #3531⋊(C3×C5) |
| unambiguous semidirect product | (C3×#3531)⋊C5 |
| Fitting, Hall | C3×#3531 ⋊ C5 |
| Sylow | #3531 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | C24⋊C5 |
| commutator, cosocle, hypocenter | #564 | C2×C3×C5 |
| Frattini | C22 | C2×C3×C24⋊C5 |
| Fitting | C3×#3531 | C5 |
| socle | C22×C3 | C2×C24⋊C5 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C2×C3×C4 | |
222 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237197);