Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1400 |
| Sylow | C5 ⋊ #67602 |
| Sylow | C3 ⋊ #10598657 |
148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^4,i^d=i^4132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4968);