Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×2−1+4 ⋊ C2 |
| Hall | C3×C5 ⋊ #454 |
| Sylow | C5 ⋊ #5245 |
| Sylow | C3 ⋊ #65534 |
292 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 75 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:
2^6,3,5|c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,h^a=h^4,d^b=df,e^b=ef,e^c=ef135 conjugacy classes — view the full character table.
| maximal subgroup of | #14316912, #14316919, #14316931, … |
| maximal normal subgroup of | #14316912, #14316919, #14316931, … |
| maximal quotient of | #14287764, #14287824, #14287863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5541);