Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×C5⋊(#120⋊C3) |
| unambiguous semidirect product | C5⋊(C3×#120⋊C3) |
| unambiguous semidirect product | #4099⋊C32 |
| unambiguous semidirect product | (C3×#4099)⋊C3 |
| Fitting | C24×C3×C5 ⋊ C2×C3 |
| derived | C24×C5 ⋊ C2×C32 |
| Hall | #4099 ⋊ C32 |
| Sylow | C5 ⋊ C3×#120⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(#120⋊C3) |
| commutator, cosocle, hypocenter | C24×C5 | C2×C32 |
| Frattini | C22 | C3×D5×A4 |
| Fitting | C24×C3×C5 | C2×C3 |
| socle | C22×C3×C5 | C2×A4 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C3 | |
172 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2543);