Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of (C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×(C22⋊C9)⋊C4 |
| unambiguous semidirect product | (C2×C22⋊C9)⋊(C4×C5) |
| derived | C22⋊C9 ⋊ C2×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | (C22⋊C9)⋊C2 |
| commutator, hypocenter | C22⋊C9 | C2×C4×C5 |
| Frattini | C2×C3 | C2×C5×S4 |
| Fitting, socle, prime radical | C24×C3×C5 | D3 |
| cosocle | C2×C22⋊C9 | C22×C5 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C22×C5 | |
220 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1518);