Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×#543⋊C3 |
| unambiguous semidirect product | (C2×#543)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#543)⋊C3 |
| Fitting, Hall | C2×C5×#543 ⋊ C3 |
| derived | #543 ⋊ C2×C3×C5 |
| Sylow | C2×#543 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | #543 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C2×C5×#543 | C3 |
| LCS | G ▷ #543 | |
| UCS | C1 ◁ C23×C5 | |
612 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237085);