Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×#578⋊C3 |
| unambiguous semidirect product | (C2×#578)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#578)⋊C3 |
| Fitting, Hall | C2×C5×#578 ⋊ C3 |
| Sylow | C2×#578 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | D4×A4 |
| commutator, cosocle | #41 | C23×C3×C5 |
| Frattini | C4 | C23×C5×A4 |
| Fitting | C2×C5×#578 | C3 |
| hypercenter | C2×C5×D8 | A4 |
| hypocenter | Q8 | C2×C3×C5×D4 |
| LCS | G ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×D8 | |
686 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237074);