Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #170⋊(C3⋊C8) |
| Hall | C3×C5 ⋊ #322 |
| Sylow | C5 ⋊ #4455 |
| Sylow | C3 ⋊ #170⋊C8 |
132 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=c,b^2=d,c^2=f,d^2=e,b^a=bf,h^a=h^2,g^b=g^2,h^c=h^496 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#170⋊C8, #14280352, C2×#170⋊(C3⋊C8), … |
| maximal normal subgroup of | D3×#170⋊C8, #14280352, C2×#170⋊(C3⋊C8), … |
| maximal quotient of | #14276695, #170⋊(C3⋊C16), #14277512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 681);