Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #380 |
| Sylow | C5 ⋊ #4942 |
| Sylow | C3 ⋊ #65501 |
468 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 160 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=e,b^a=be,c^a=cf,h^a=h^4,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #14297523, #14297524, #14297534, … |
| maximal normal subgroup of | #14297523, #14297524, #14297534, … |
| maximal quotient of | #14279877, #14279913, #14279939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3708);