Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×#578⋊C3 |
| unambiguous semidirect product | (D5×#578)⋊C3 |
| Fitting | C5×#578 ⋊ C2×C3 |
| Hall | D5×#578 ⋊ C3 |
| Sylow | C5 ⋊ C2×#578⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D5×A4 |
| commutator, cosocle | C5×#41 | C23×C3 |
| Frattini | C4 | C22×D5×A4 |
| Fitting | C5×#578 | C2×C3 |
| socle | C2×C5 | C2×D4×A4 |
| hypercenter | D8 | D5×A4 |
| hypocenter | C5×Q8 | C2×C3×D4 |
| LCS | G ▷ C5×#41 ▷ C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
686 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239867);