Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q64 |
| Sylow | C5 ⋊ #4522 |
| Sylow | C3 ⋊ Dic80 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #90938 |
| commutator, Fitting, cosocle | C3×C5×C16 | C22 |
| Frattini, hypercenter | C16 | D3×D5 |
| socle, prime radical | C2×C3×C5 | D16 |
| hypocenter | C3×C5 | Q64 |
| LCS | G ▷ C3×C5×C16 ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=cd,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,h^a=h^4,g^b=g^2126 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4522, #14319192, C2×#11745828, … |
| maximal normal subgroup of | D5×#4522, #14319192, C2×#11745828, … |
| maximal quotient of | #14279595, #14279596, #14279723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 23);