Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #456 |
| Sylow | C5 ⋊ #5095 |
| Sylow | C3 ⋊ #65494 |
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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,c^2=f,e^2=f,c^a=cd,e^a=ef,h^a=h^4,c^b=ce,d^b=df,e^b=ef,g^b=g^2,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | #14425144, D3×#65494, D5×#5095, … |
| maximal normal subgroup of | #14425144, D3×#65494, D5×#5095, … |
| maximal quotient of | #14288056, #14288061, #14288113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3609);