Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #563 |
| Sylow | C5 ⋊ #5699 |
| Sylow | C3 ⋊ #66006 |
392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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=f,c^2=ef,d^2=f,c^a=cf,d^a=def,h^a=h^4,c^b=ce,d^b=df,g^b=g^293 conjugacy classes — view the full character table.
| maximal subgroup of | #14290952, #14290967, #14290970, … |
| maximal normal subgroup of | #14290952, #14290967, #14290970, … |
| maximal quotient of | #14330822, #14331077, #14331078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6848);