Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×C4×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #433 |
| Sylow | C5 ⋊ #4690 |
| Sylow | C3 ⋊ #64979 |
192 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 75 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=e,c^2=d,d^2=f,b^a=bf,c^a=ce,g^a=g^2,h^a=h^4252 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#433, C2×#11750791, D5×#4690, … |
| maximal normal subgroup of | D15×#433, C2×#11750791, D5×#4690, … |
| maximal quotient of | #14294925, #14295088, #14296182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4986);