Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ M64 |
| Sylow | C5 ⋊ #4499 |
| Sylow | C3 ⋊ #64667 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D3×D5 |
| commutator, socle | C2×C3×C5 | C2×C16 |
| Fitting, cosocle | C3×C5×C16 | C22 |
| prime radical | C2×C3×D5 | C16 |
| hypocenter | C3×C5 | M64 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C16 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,h^a=h^4,g^b=g^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #14279235, #14279236, #14279237, … |
| maximal normal subgroup of | #14279235, #14279236, #14279237, … |
| maximal quotient of | #14279211, #14279251, #14279693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10);