Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #450 |
| Sylow | C5 ⋊ #4776 |
| Sylow | C3 ⋊ #65065 |
376 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 68 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=ef,d^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=cde,d^b=df,g^b=g^2,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4776, D3×#65065, #14423254, … |
| maximal normal subgroup of | D5×#4776, D3×#65065, #14423254, … |
| maximal quotient of | #14287994, #14288135, #14288558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1679);