Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #1285 |
| Sylow | C5 ⋊ #67750 |
| Sylow | C3 ⋊ #10598585 |
328 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 85 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=d,b^2=e,c^2=fg,d^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^2,i^a=i^3,d^b=dg,h^b=h^2,i^b=i^2,i^d=i^4,i^e=i^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2639);