Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×#107 ⋊ C2 |
| Hall | C3×C5 ⋊ #480 |
| Sylow | C5 ⋊ #4882 |
| Sylow | C3 ⋊ #65171 |
228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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=d,c^2=ef,e^2=f,c^a=cd,g^a=g^2,h^a=h^4,c^b=ce,e^b=ef117 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#480, C2×#11750983, D5×#4882, … |
| maximal normal subgroup of | D15×#480, C2×#11750983, D5×#4882, … |
| maximal quotient of | #14298428, #14299348, #14300684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5178);