Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×Q16 ⋊ C22 |
| Hall | C3×C5 ⋊ #576 |
| Sylow | C5 ⋊ #5769 |
| Sylow | C3 ⋊ #66103 |
536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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|c^2=f,d^2=f,e^2=f,b^a=bf,c^a=cf,d^a=df,h^a=h^4,c^b=cf,d^b=df,g^b=g^2,d^c=de,e^c=ef,e^d=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #14478506, #14478507, #14478508, … |
| maximal normal subgroup of | #14478506, #14478507, #14478508, … |
| maximal quotient of | #14412694, #14413514, #14417140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8310);