Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #95⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×#376⋊C3 |
| unambiguous semidirect product | (C2×#376)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#376)⋊C3 |
| Fitting, Hall | C2×C5×#376 ⋊ C3 |
| Sylow | C2×#376 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C5 | C42⋊C3 |
| commutator, cosocle, hypocenter | #95 | C22×C3×C5 |
| Frattini | C23 | C22×C5×A4 |
| Fitting | C2×C5×#376 | C3 |
| socle | C24×C5 | C2×A4 |
| prime radical | C2×C5×#95⋊C3 | C2 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C4×C5 | |
350 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236583);