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 ⋊ #416 |
| Sylow | C5 ⋊ #5113 |
| Sylow | C3 ⋊ #65794 |
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 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) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=f,d^2=f,e^2=f,b^a=be,h^a=h^2,d^b=df,e^b=ef,g^b=g^2,h^d=h^478 conjugacy classes — view the full character table.
| maximal subgroup of | #14295970, #14295971, #14295976, … |
| maximal normal subgroup of | #14295970, #14295971, #14295976, … |
| maximal quotient of | #14281605, #14281606, #14281613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5899);