Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(#585⋊C5) |
| unambiguous semidirect product | #5968⋊C5 |
| Hall | #5968 ⋊ C5 |
| Sylow | C3 ⋊ #585⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C3×2−1+4 | C2×C5 |
| socle | C2×C3 | C2×C24⋊C5 |
| LCS | G ▷ C3×2−1+4 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2,5,2^4,3,2|a^2=h,c^2=h,e^2=h,f^2=h,g^a=g^2,c^b=e,d^b=de,e^b=ef,f^b=cdf,d^c=dh,e^c=eh,f^c=fh,e^d=eh,f^d=fh,f^e=fh39 conjugacy classes — view the full character table.
| maximal subgroup of | #14514341, #14514342, #14514343, … |
| maximal normal subgroup of | #14514341, #14514342, #14514343, … |
| maximal quotient of | C3⋊(#3531⋊C5), Dic3×2−1+4⋊C5, C2×C3⋊(#585⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11001);