Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊(#126⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C22×C5⋊(#126⋊C3) |
| Fitting | C22×C42×C5 ⋊ C2×C3 |
| derived | C42×C5 ⋊ C23×C3 |
| Hall | C22×#4022 ⋊ C3 |
| Sylow | C5 ⋊ C22×#126⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊(#126⋊C3) |
| commutator, cosocle, hypocenter | C42×C5 | C23×C3 |
| Frattini | C22 | C22×D5×A4 |
| Fitting | C22×C42×C5 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 ◁ C22 | |
600 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239673);