Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×#121 ⋊ C2 |
| Hall | C3×C5 ⋊ #466 |
| Sylow | C5 ⋊ #5038 |
| Sylow | C3 ⋊ #65327 |
268 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 77 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|d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^4,c^b=ce,d^c=df120 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#466, C2×#11751139, D5×#5038, … |
| maximal normal subgroup of | D15×#466, C2×#11751139, D5×#5038, … |
| maximal quotient of | #14291408, #14291447, #14291690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5334);