Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×#104 ⋊ C2 |
| Hall | C3×C5 ⋊ #443 |
| Sylow | C5 ⋊ #4824 |
| Sylow | C3 ⋊ #65113 |
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=h^4,c^b=cef,e^b=ef,e^c=ef126 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#443, C2×#11750925, D5×#4824, … |
| maximal normal subgroup of | D15×#443, C2×#11750925, D5×#4824, … |
| maximal quotient of | #14286065, #14286124, #14286142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5120);