Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×Q32 ⋊ C2 |
| Hall | C3×C5 ⋊ #508 |
| Sylow | C5 ⋊ #4919 |
| Sylow | C3 ⋊ #65208 |
168 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,c^2=f,d^2=ef,e^2=f,b^a=bf,c^a=cf,g^a=g^2,h^a=h^4,c^b=cd,d^b=de,e^b=ef,d^c=de,e^c=ef99 conjugacy classes — view the full character table.
| maximal subgroup of | #14319208, #14319214, #14319231, … |
| maximal normal subgroup of | #14319208, #14319214, #14319231, … |
| maximal quotient of | #14313848, #14314586, #14315306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5215);