Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×C22⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #543 |
| Sylow | C5 ⋊ #5634 |
| Sylow | C3 ⋊ #65968 |
484 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 147 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,d^2=f,d^a=de,g^a=g^2,h^a=h^4,c^b=ce,d^c=df120 conjugacy classes — view the full character table.
| maximal subgroup of | #14287716, #14287725, #14287733, … |
| maximal normal subgroup of | #14287716, #14287725, #14287733, … |
| maximal quotient of | #14322795, #14322801, #14324437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10588);