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 ⋊ #577 |
| Sylow | C5 ⋊ #5770 |
| Sylow | C3 ⋊ #66112 |
516 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| 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,d^b=df,g^b=g^2,d^c=de,e^c=ef,e^d=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | #14510046, D3×#66112, D5×#5770, … |
| maximal normal subgroup of | #14510046, D3×#66112, D5×#5770, … |
| maximal quotient of | #14412692, #14412734, #14413487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8309);