Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #73046 |
384 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=d,b^2=cd,c^2=e,b^a=bc,g^a=g^4,c^b=ce,d^b=de,f^b=f^2,h^b=hi,h^f=i,i^f=hi100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237454);