Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #471 |
| Sylow | C5 ⋊ #5177 |
| Sylow | C3 ⋊ #65492 |
208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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|c^2=f,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,h^a=h^4,c^b=ce,e^b=ef,g^b=g^2,d^c=df,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5177, D3×#65492, C2×#11749385, … |
| maximal normal subgroup of | D5×#5177, D3×#65492, C2×#11749385, … |
| maximal quotient of | #14291318, #14291381, #14291582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3580);