Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #510 |
| Sylow | C5 ⋊ #5195 |
| Sylow | C3 ⋊ #65198 |
164 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 56 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|b^2=de,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,h^a=h^4,c^b=cf,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #14315771, #14315784, #14315787, … |
| maximal normal subgroup of | #14315771, #14315784, #14315787, … |
| maximal quotient of | #14313916, #14313986, #14314648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1749);