Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #496 |
| Sylow | C5 ⋊ #5154 |
| Sylow | C3 ⋊ #65465 |
288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 288 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) = 480 |
Polycyclic presentation:
2^6,3,5|c^2=ef,e^2=f,b^a=bd,c^a=ce,e^a=ef,h^a=h^4,c^b=cef,e^b=ef,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65465, D5×#5154, #14438983, … |
| maximal normal subgroup of | D3×#65465, D5×#5154, #14438983, … |
| maximal quotient of | #14293676, #14293703, #14293733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2210);