Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×#390 ⋊ C2 |
| Hall | C3×C5 ⋊ #2006 |
| Sylow | C5 ⋊ #69664 |
| Sylow | C3 ⋊ #10600457 |
812 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,h^b=h^2,i^b=i^4,e^c=eg,h^c=h^2,i^c=i^4222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 33683);