Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#41 ⋊ C4 |
| Hall | C3×C5 ⋊ #520 |
| Sylow | C5 ⋊ #5827 |
| Sylow | C3 ⋊ #66266 |
588 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=e,d^2=f,d^a=df,g^a=g^2,h^a=h^3,c^b=cf,h^e=h^484 conjugacy classes — view the full character table.
| maximal subgroup of | #14299729, #14299772, #14299800, … |
| maximal normal subgroup of | #14299729, #14299772, #14299800, … |
| maximal quotient of | #14319673, #14319724, #14319776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11190);