Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #481 |
| Sylow | C5 ⋊ #4777 |
| Sylow | C3 ⋊ #65152 |
228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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=e,c^2=ef,d^2=f,b^a=be,c^a=cd,d^a=df,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4777, #14431711, D3×#65152, … |
| maximal normal subgroup of | D5×#4777, #14431711, D3×#65152, … |
| maximal quotient of | #14298479, #14299412, #14300703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1527);