Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C22×C5×#120⋊C3 |
| Fitting, Hall | C22×C5×#120 ⋊ C3 |
| derived | C24 ⋊ C23×C3×C5 |
| Sylow | C22×#120 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #120⋊C3 |
| commutator, cosocle, hypocenter | C24 | C23×C3×C5 |
| Frattini | C22 | C23×C5×A4 |
| Fitting | C22×C5×#120 | C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C22×C5 | |
1708 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237018);