Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #10617514⋊C3 |
| Fitting | C22×C5×Q8 ⋊ C3×C4 |
| Hall | #10617514 ⋊ C3 |
| Sylow | C5 ⋊ #2884⋊C3 |
382 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^2,3,2^4,5,2|a^2=d,f^2=i,g^2=i,b^a=be,e^a=ei,h^a=h^2,d^b=di,f^c=fg,g^c=f,h^d=h^4,g^f=gi71 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238265);