Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊(A4⋊C16) |
| derived | C5×A4 ⋊ C2×C16 |
| Sylow | C5 ⋊ C2×A4⋊C16 |
230 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=c,b^2=d,c^2=d,d^2=e,f^a=f^2,g^a=g^2,h^a=hi,g^c=g^4,h^f=i,i^f=hi112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238155);