Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ #4078 |
| Sylow | C5 ⋊ #63825 |
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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:
2^5,3^2,5|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,h^a=h^4,c^b=ce,d^b=de,f^b=f^2,g^b=g^2123 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63825, #72230427, #72230429 |
| maximal normal subgroup of | D5×#63825, #72230427, #72230429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3971);