Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10604774⋊C3 |
| Hall | #10604774 ⋊ C3 |
| Sylow | C5 ⋊ #2258⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | A4×AGL(1,𝔽5) |
| commutator, hypocenter | C5×Q8 | C3×C16 |
| Fitting | C5×#131 | C3×C4 |
| socle | C2×C5 | A4×C16 |
| prime radical | C5×#41⋊C3 | C8 |
| cosocle | #65429 | C2×C3 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C8 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2,3,2^5,5,2|a^2=c,c^2=d,d^2=e,e^2=i,f^2=i,g^2=i,h^a=h^2,f^b=fg,g^b=f,h^c=h^4,g^f=gi140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237300);