Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ #578 |
| Sylow | C5 ⋊ #5766 |
| Sylow | C3 ⋊ #66100 |
496 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 139 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|c^2=f,d^2=f,e^2=f,b^a=bf,g^a=g^2,h^a=h^4,d^c=de,e^c=ef,e^d=ef120 conjugacy classes — view the full character table.
| maximal subgroup of | #14316447, #14316459, #14316491, … |
| maximal normal subgroup of | #14316447, #14316459, #14316491, … |
| maximal quotient of | #14412703, #14413496, #14417158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10720);