Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C2×C4⋊C8 |
| Sylow | C5 ⋊ D3×C4⋊C8 |
| Sylow | C3 ⋊ D5⋊(C4⋊C8) |
276 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 92 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=d,b^2=f,c^2=ef,d^2=f,c^a=ce,h^a=h^2,g^b=g^2,h^d=h^484 conjugacy classes — view the full character table.
| maximal subgroup of | #14284531, #14284566, #14284614, … |
| maximal normal subgroup of | #14284531, #14284566, #14284614, … |
| maximal quotient of | #14285505, #14285536, #14285580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6079);