Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1393 |
| Sylow | C5 ⋊ #67641 |
| Sylow | C3 ⋊ #10598568 |
464 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 72 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:
2^7,3,5|a^2=d,b^2=e,c^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dfg,i^b=i^2,d^c=dg,i^e=i^475 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4824);