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 ⋊ #5205 |
| Sylow | C3 ⋊ #65041 |
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|b^2=f,c^2=d,d^2=f,c^a=cd,d^a=df,e^a=ef,h^a=h^4,c^b=ce,d^b=df,g^b=g^2,e^c=ef69 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5205, #14425147, D3×#65041, … |
| maximal normal subgroup of | D5×#5205, #14425147, D3×#65041, … |
| maximal quotient of | #14288076, #14288095, #14288130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2448);