Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C22×C4⋊(C5⋊S4) |
| Fitting | C24×C4×C5 ⋊ D3 |
| Sylow | C5 ⋊ C22×C4⋊S4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×C5⋊S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Frattini | C2 | C23×C5⋊S4 |
| Fitting | C24×C4×C5 | D3 |
| socle | C25×C5 | C2×D3 |
| hypercenter | C22×C4 | C5⋊S4 |
| hypocenter | C5×A4 | C22×D4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
2582 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 2582 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240289);