Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #488 |
| Sylow | C5 ⋊ #5068 |
| Sylow | C3 ⋊ #65057 |
192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 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|a^2=d,b^2=de,c^2=d,e^2=f,c^a=cdf,h^a=h^4,c^b=ce,g^b=g^2,e^c=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65057, #14437738, C2×#11747142, … |
| maximal normal subgroup of | D3×#65057, #14437738, C2×#11747142, … |
| maximal quotient of | #14298845, #14304503, #14304537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1337);