Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #440 |
| Sylow | C5 ⋊ #5164 |
| Sylow | C3 ⋊ #65453 |
240 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=f,e^2=f,c^a=cf,g^a=g^2,h^a=h^4,c^b=ce,e^b=ef,e^c=ef120 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#440, C2×#11751265, D5×#5164, … |
| maximal normal subgroup of | D15×#440, C2×#11751265, D5×#5164, … |
| maximal quotient of | SD16⋊(C3⋊#168), #14286883, #14287168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5460);