Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊#857 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×C5⋊#857 |
| unambiguous semidirect product | C5⋊(C3×#857) |
| Fitting | C3×C42×C5 ⋊ D3 |
| derived | C5×C42⋊C3 ⋊ C2×C3 |
| Sylow | C5 ⋊ C3×#857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊#857 |
| commutator, cosocle, hypocenter | C5×C42⋊C3 | C2×C3 |
| Frattini | C22 | C3×C5⋊S4 |
| Fitting | C3×C42×C5 | D3 |
| socle | C22×C3×C5 | S4 |
| LCS | G ▷ C5×C42⋊C3 | |
| UCS | C1 ◁ C3 | |
102 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 180 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2525);