Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×D8 |
| Sylow | C5 ⋊ #4756 |
| Sylow | C3 ⋊ C4×#686 |
268 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 268 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,e^2=f,c^a=ce,e^a=ef,h^a=h^4,g^b=g^2,e^c=ef102 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4756, D8×#1200, C4×D3×#686, … |
| maximal normal subgroup of | D5×#4756, D8×#1200, C4×D3×#686, … |
| maximal quotient of | #14286092, #14286526, #14286545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3181);