Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #447 |
| Sylow | C5 ⋊ #4773 |
| Sylow | C3 ⋊ #65325 |
396 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=ce,g^b=g^2,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4773, #14423194, D3×#65325, … |
| maximal normal subgroup of | D5×#4773, #14423194, D3×#65325, … |
| maximal quotient of | #14287713, #14287854, #14288277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1677);