Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×C5×D4 ⋊ C4 |
| Hall | C32×C5 ⋊ #104 |
| Sylow | C32 ⋊ #4008 |
| Sylow | C5 ⋊ #63783 |
168 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,d^2=e,b^a=bd,f^a=fg,g^a=fg^2,h^a=h^2,c^b=ce,d^b=de,f^c=f^2,g^c=g^2,h^c=h^469 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2701);