Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43×C5 · Schur multiplier (H2) = C23×C43 |
| direct product | C43×C5×D3 |
| Fitting | C3×C43×C5 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C43×C5 |
| Hall | C3×C5 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43×C5 | D3 |
| commutator, hypocenter | C3 | C2×C43×C5 |
| Frattini | C23 | C23×C5×D3 |
| Fitting | C3×C43×C5 | C2 |
| socle | C23×C3×C5 | C24 |
| prime radical | C23×C5×D3 | C23 |
| cosocle | C23×C3 | C24×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C43×C5 | |
2544 conjugacy classes of subgroups; only the 1530 normal subgroups are shown.
This group has 2544 conjugacy classes of subgroups — too many to draw. Only its 1530 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45015);