Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #391 |
| Sylow | C5 ⋊ #4929 |
| Sylow | C3 ⋊ #65263 |
372 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 144 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=d,b^2=def,c^2=f,b^a=be,h^a=h^4,c^b=cf,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #14276688, #14297240, #14297252, … |
| maximal normal subgroup of | #14276688, #14297240, #14297252, … |
| maximal quotient of | #14279940, #14279981, #14280142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2782);