Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×C5⋊#1020 |
| unambiguous semidirect product | C5⋊(C3×#1020) |
| Fitting, socle | C24×C3×C5 ⋊ D3 |
| derived | C5×C22⋊A4 ⋊ C2×C3 |
| Sylow | C5 ⋊ C3×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊#1020 |
| commutator, cosocle, hypocenter | C5×C22⋊A4 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | D3 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C3 | |
238 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 26 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.
| maximal subgroup of | C3×D5×#1020, D3×C5⋊#1020, #72231058, … |
| maximal normal subgroup of | C3×D5×#1020, D3×C5⋊#1020, #72231058 |
| maximal quotient of | C3×C5⋊#5935, C3×C3⋊(C5⋊#1020), #72269556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5930);