Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C3⋊C8×C24⋊C5 |
| unambiguous semidirect product | C3⋊(C8×C24⋊C5) |
| unambiguous semidirect product | (C24×C3⋊C8)⋊C5 |
| derived | C24×C3 ⋊ C5×C8 |
| Hall | C24×C3⋊C8 ⋊ C5 |
| Sylow | C3 ⋊ C8×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×C24⋊C5 |
| commutator, hypocenter | C24×C3 | C5×C8 |
| Fitting, cosocle | C24×C3×C4 | C2×C5 |
| socle | C25×C3 | C4×C5 |
| prime radical | C2×C3×C24⋊C5 | C4 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C4 | |
424 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239379);