Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×AGL(1,ℤ/8) ⋊ C2 |
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ #5199 |
| Sylow | C3 ⋊ #65488 |
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^2,h^a=h^4,c^b=ce,e^b=ef,d^c=df,e^c=ef93 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#472, C2×#11751300, D5×#5199, … |
| maximal normal subgroup of | D15×#472, C2×#11751300, D5×#5199, … |
| maximal quotient of | #14291408, #14291447, #14291768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5495);