Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of S4×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | S4×Dic15 |
| unambiguous semidirect product | (C3×S4)⋊Dic5 |
| derived | C3×C5×A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ Dic3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×D15 |
| commutator, hypocenter | C3×C5×A4 | C2×C4 |
| Fitting, socle | C23×C3×C5 | C2×D3 |
| prime radical | C2×C3×C5×S4 | C2 |
| cosocle | C2×C3×C5×A4 | C22 |
| LCS | G ▷ C3×C5×A4 | |
| UCS | C1 ◁ C2 | |
236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4872);