Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #556 |
| Sylow | C5 ⋊ #5533 |
| Sylow | C3 ⋊ #65867 |
424 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 130 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|c^2=f,d^2=ef,b^a=be,d^a=df,h^a=h^4,d^b=df,g^b=g^2,d^c=df105 conjugacy classes — view the full character table.
| maximal subgroup of | #14460000, #14460033, #14460035, … |
| maximal normal subgroup of | #14460000, #14460033, #14460035, … |
| maximal quotient of | #14326946, #14326948, #14327714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 7998);