Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×Dic5×S4 |
| derived | C5×A4 ⋊ C2×C3×C4 |
| Sylow | C5 ⋊ C3×C4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×S4 |
| commutator, hypocenter | C5×A4 | C2×C3×C4 |
| Frattini | C2 | C3×D5×S4 |
| Fitting, socle | C23×C3×C5 | C2×D3 |
| prime radical | C2×C3×C5×S4 | C2 |
| cosocle | C2×C5×A4 | C22×C3 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C3 | |
236 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4827);