Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2884 |
| Sylow | C5 ⋊ #82556 |
| Sylow | C3 ⋊ #10617514 |
1432 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1432 conjugacy classes of subgroups — too many to draw. Only its 294 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|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,i^a=i^2,f^b=fg,h^b=h^2,d^c=dg,i^f=i^4105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 137732);