Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C22⋊C16 |
| Sylow | C5 ⋊ #4549 |
| Sylow | C3 ⋊ C22⋊#672 |
132 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 75 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,g^a=g^2,h^a=h^4264 conjugacy classes — view the full character table.
| maximal subgroup of | #14277518, #14277521, #14277526, … |
| maximal normal subgroup of | #14277518, #14277521, #14277526, … |
| maximal quotient of | #14277521, #14277641, D4⋊(C3⋊#672), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 565);