Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊#10619373 |
| Fitting | C3×2−1+4 ⋊ AGL(1,𝔽5) |
| derived | C3×2−1+4⋊C5 ⋊ C4 |
| Sylow | C3 ⋊ #10619373 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#66297 |
| commutator, hypocenter | C3×2−1+4⋊C5 | C4 |
| Fitting | C3×2−1+4 | AGL(1,𝔽5) |
| socle | C2×C3 | #66297 |
| prime radical, cosocle | C3×#66244 | C2 |
| LCS | G ▷ C3×2−1+4⋊C5 | |
| UCS | C1 ◁ C2 | |
106 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^2,3,5,2^5|a^2=b,f^2=i,g^2=i,c^a=c^2,d^a=d^2,e^a=egi,f^a=fhi,g^a=fgh,h^a=hi,d^b=d^4,e^b=efh,f^b=fi,g^b=ghi,e^d=efgi,f^d=ef,g^d=gh,h^d=eg,g^e=gi,h^e=hi,g^f=gi30 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240037);