Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ #5199 |
| Sylow | C3 ⋊ #65431 |
216 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 60 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|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,h^a=h^4,g^b=g^2,e^c=ef87 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5199, #14429392, D3×#65431, … |
| maximal normal subgroup of | D5×#5199, #14429392, D3×#65431, … |
| maximal quotient of | #14291432, #14291471, #14291792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3640);