Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #455 |
| Sylow | C5 ⋊ #5061 |
| Sylow | C3 ⋊ #65531 |
304 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,d^b=df,e^b=ef,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #14279336, #14279338, #14316694, … |
| maximal normal subgroup of | #14279336, #14279338, #14316694, … |
| maximal quotient of | #14287983, #14288022, #14288211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3342);