Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C32×C4×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C2×C4⋊C4 |
| Sylow | C32 ⋊ C2×C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #63900 |
422 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 422 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) = 120 |
Polycyclic presentation:
2^5,3^2,5|a^2=d,c^2=e,c^a=ce,f^a=f^2,h^a=h^2,f^b=f^2,g^b=g^2,h^d=h^472 conjugacy classes — view the full character table.
| maximal subgroup of | #72230209, AGL(1,𝔽5)×#3802, D32×C4⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #72230209, AGL(1,𝔽5)×#3802, D32×C4⋊AGL(1,𝔽5), … |
| maximal quotient of | #72260236 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5050);