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×Q8 ⋊ C4 |
| Hall | C32×C5 ⋊ #103 |
| Sylow | C32 ⋊ #3967 |
| Sylow | C5 ⋊ #63784 |
160 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 33 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,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=fg,g^a=fg^2,h^a=h^4,d^b=de,f^c=f^2,g^c=g^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2679);