Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C4⋊(C5⋊#1020) |
| Fitting | C24×C4×C5 ⋊ D3 |
| Sylow | C5 ⋊ C4⋊#1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C5⋊#1020 |
| commutator, cosocle | C2×C5×C22⋊A4 | C22 |
| Fitting | C24×C4×C5 | D3 |
| socle | C25×C5 | C2×D3 |
| hypercenter | C4 | C5⋊#1020 |
| hypocenter | C5×C22⋊A4 | D4 |
| LCS | G ▷ C2×C5×C22⋊A4 ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C2 ◁ C4 | |
870 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 870 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5,2^4|b^2=c,b^a=bc,d^a=d^2,e^a=e^4,f^a=fg,h^a=hi,f^d=g,g^d=fg,h^d=i,i^d=hi92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240320);