Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C22×A4×C22⋊D5 |
| Fitting | C26×C5 ⋊ C2×C3 |
| Hall | C24×C22⋊D5 ⋊ C3 |
| Sylow | C5 ⋊ C22×D4×A4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D5×A4 |
| commutator, cosocle | C23×C5 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C26×C5 | C2×C3 |
| socle | C25×C5 | C22×C3 |
| hypercenter | C24 | D5×A4 |
| hypocenter | C22×C5 | C22×C3×D4 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
4304 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 4304 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240371);