Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C9 ⋊ #137 |
| Sylow | C9 ⋊ #4064 |
| Sylow | C5 ⋊ #63480 |
180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3,5,3|a^2=e,b^2=e,c^2=e,d^2=e,f^3=h,c^a=cd,d^a=de,g^a=g^4,c^b=cde,d^b=de,f^b=f^2h^2,h^b=h^2,d^c=de93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 596);