Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×#226 |
| Sylow | C5 ⋊ D3×#226 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×D15 |
| commutator, cosocle, hypocenter | C3×C5×SL(2,𝔽3) | C22 |
| Fitting | C3×C5×Q8 | C2×D3 |
| socle | C2×C3×C5 | C2×S4 |
| prime radical | SL(2,𝔽3)×D15 | C2 |
| LCS | G ▷ C3×C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
166 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4867);