Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #68006 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | A4⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×SL(2,𝔽3) | C16 |
| Fitting | C5×#131 | Dic3 |
| socle | C2×C5 | A4⋊C16 |
| prime radical | C5×#41⋊C3 | C8 |
| cosocle | #65429⋊C3 | C2 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C8 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^4,3,5,2^3|a^2=b,b^2=c,c^2=d,d^2=i,g^2=i,h^2=i,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,f^b=f^4,g^e=h,h^e=ghi,h^g=hi92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237285);