Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q82 |
| Sylow | C5 ⋊ #5722 |
| Sylow | C3 ⋊ #66056 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×C4⋊Q8 | C2 |
| hypercenter | C4⋊Q8 | D15 |
| hypocenter | C3×C5 | Q82 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
424 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=f,c^2=e,d^2=ef,b^a=bf,g^a=g^2,h^a=h^4,d^b=df,d^c=de123 conjugacy classes — view the full character table.
| maximal subgroup of | #14289009, #14289018, #14289026, … |
| maximal normal subgroup of | #14289009, #14289018, #14289026, … |
| maximal quotient of | #14327210, #14327216, #14329823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10676);