Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×C22⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #458 |
| Sylow | C5 ⋊ #4742 |
| Sylow | C3 ⋊ #65031 |
320 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=de,c^a=cd,e^a=ef,h^a=h^4,c^b=ce,d^b=df,g^b=g^2,d^c=df,e^c=ef69 conjugacy classes — view the full character table.
| maximal subgroup of | #14425637, D5×#4742, D3×#65031, … |
| maximal normal subgroup of | #14425637, D5×#4742, D3×#65031, … |
| maximal quotient of | #14288272, #14288274, #14288276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1331);