Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#819 |
| Hall | C3×C5 ⋊ C2×#108 |
| Sylow | C5 ⋊ C2×#819 |
| Sylow | C3 ⋊ D5⋊#108 |
212 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 212 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,b^2=f,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^3,h^d=h^4108 conjugacy classes — view the full character table.
| maximal subgroup of | #14278839, #14278845, #14278860, … |
| maximal normal subgroup of | #14278839, #14278845, #14278860, … |
| maximal quotient of | D5⋊#4457, D5⋊#4458, #14285551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6578);