Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(#3573⋊C5) |
| unambiguous semidirect product | #87296⋊C5 |
| Hall | #87296 ⋊ C5 |
| Sylow | C3 ⋊ #3573⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×C24⋊C5 |
| commutator, hypocenter | C3×2−1+4 | C4×C5 |
| Fitting, cosocle | C3×#585 | C2×C5 |
| socle | C2×C3 | C4×C24⋊C5 |
| prime radical | C3×#585⋊C5 | C2 |
| LCS | G ▷ C3×2−1+4 | |
| UCS | C1 ◁ C4 | |
310 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2,5,2^5,3,2|a^2=c,c^2=i,d^2=i,e^2=i,f^2=i,h^a=h^2,d^b=de,e^b=df,f^b=defgi,g^b=degi,e^d=ei,f^d=fi,g^d=gi,f^e=fi78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239381);