Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#812 |
| Hall | C3×C5 ⋊ C2×M32 |
| Sylow | C5 ⋊ C2×#812 |
| Sylow | C3 ⋊ D5⋊M32 |
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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|a^2=d,c^2=e,d^2=e,e^2=f,b^a=bf,g^a=g^2,h^a=h^3,h^d=h^4120 conjugacy classes — view the full character table.
| maximal subgroup of | #14278723, #14278731, #14278742, … |
| maximal normal subgroup of | #14278723, #14278731, #14278742, … |
| maximal quotient of | #14312555, #14312592, #14312596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6569);