Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(#401⋊C3) |
| unambiguous semidirect product | (C2×C5)⋊(#401⋊C3) |
| unambiguous semidirect product | (C2×C5⋊#401)⋊C3 |
| Hall | C2×C5⋊#401 ⋊ C3 |
| Sylow | C5 ⋊ C2×#401⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊(#126⋊C3) |
| commutator, cosocle, hypocenter | C5×#95 | C22×C3 |
| Frattini | C23 | C2×D5×A4 |
| Fitting | C2×C5×#95 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| prime radical | C2×C5×#95⋊C3 | C2 |
| LCS | G ▷ C5×#95 | |
| UCS | C1 ◁ C22 | |
242 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237781);