Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×Q8 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×SD16 |
| Sylow | C5 ⋊ #4788 |
| Sylow | C3 ⋊ SD16×AGL(1,𝔽5) |
244 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 244 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) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=f,e^2=f,c^a=ce,e^a=ef,h^a=h^2,c^b=ce,e^b=ef,g^b=g^2,e^c=ef,h^d=h^454 conjugacy classes — view the full character table.
| maximal subgroup of | D3×SD16×AGL(1,𝔽5), C2×#11751965, #14416303, … |
| maximal normal subgroup of | D3×SD16×AGL(1,𝔽5), C2×#11751965, #14416303, … |
| maximal quotient of | #14286193, #14286194, #14286201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6160);