Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #399 |
| Sylow | C5 ⋊ #4949 |
| Sylow | C3 ⋊ #64966 |
372 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 108 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=df,c^2=ef,b^a=bd,c^a=ce,h^a=h^4,c^b=cf,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #14278297, #14278299, #14288544, … |
| maximal normal subgroup of | #14278297, #14278299, #14288544, … |
| maximal quotient of | #14280076, #14280080, #14280252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2969);