Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #419 |
| Sylow | C5 ⋊ #4802 |
| Sylow | C3 ⋊ #65091 |
300 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 78 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=e,b^2=ef,c^2=de,d^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=cdf,d^b=df,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4802, D3×#65091, #14412446, … |
| maximal normal subgroup of | D5×#4802, D3×#65091, #14412446, … |
| maximal quotient of | #14281754, #14282052, #14282350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1839);