Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #73049 |
500 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 36 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=c,b^2=e,b^a=bd,d^a=de,g^a=g^2,c^b=ce,f^b=f^2,h^b=hi,g^c=g^4,h^f=i,i^f=hi52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238120);