Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ((C24⋊C5)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10617015⋊C3 |
| derived | C24⋊C5 ⋊ C3×C8 |
| Hall | #10617015 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | ((C24⋊C5)⋊C2)⋊C3 |
| commutator, hypocenter | C24⋊C5 | C3×C8 |
| Fitting | C24×C4 | C3×D5 |
| socle | C25 | C3×Dic5 |
| prime radical | C2×AGL(1,𝔽16) | C4 |
| cosocle | C4×C24⋊C5 | C2×C3 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C4 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^2,5,2^4|a^2=c,c^2=d,e^a=e^4,f^a=fg,h^a=hi,f^b=fhi,g^b=gi,h^b=fg,i^b=g,f^e=fg,g^e=gh,h^e=fgi,i^e=fghi56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238044);