Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C4×C3⋊Dic15 |
| derived, Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C2×C4×Dic5 |
| Sylow | C5 ⋊ C2×C4×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C2×C42 |
| Frattini | C22 | C22×C3⋊D15 |
| Fitting | C22×C32×C4×C5 | C2 |
| socle, prime radical | C23×C32×C5 | C22 |
| cosocle | C22×C32×C5 | C23 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22×C4 | |
648 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1440 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4508);