Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #428 |
| Sylow | C5 ⋊ #4881 |
| Sylow | C3 ⋊ #65150 |
236 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 80 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=d,c^2=ef,e^2=f,c^a=ce,e^a=ef,h^a=h^4,c^b=cef,e^b=ef,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65150, D5×#4881, #14413364, … |
| maximal normal subgroup of | D3×#65150, D5×#4881, #14413364, … |
| maximal quotient of | #14285613, #14285781, #14285973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1835);