Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #350 |
| Sylow | C5 ⋊ #4515 |
| Sylow | C3 ⋊ #64735 |
112 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^2,h^a=h^4,d^b=df168 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#350, C2×#11746336, D5×#4515, … |
| maximal normal subgroup of | D15×#350, C2×#11746336, D5×#4515, … |
| maximal quotient of | #14277533, #14277653, #14277751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 531);