Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#672 |
| Hall | C3×C5 ⋊ C22⋊C16 |
| Sylow | C5 ⋊ (C2×D3)⋊C16 |
| Sylow | C3 ⋊ C22⋊#672 |
132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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=c,c^2=e,e^2=f,b^a=bd,h^a=h^4,g^b=g^2168 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(C2×D3)⋊C16, #14312805, D3×C22⋊#672, … |
| maximal normal subgroup of | D5×(C2×D3)⋊C16, #14312805, D3×C22⋊#672, … |
| maximal quotient of | #14277528, #14277648, #14277764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 75);