Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #407 |
| Sylow | C5 ⋊ #4726 |
| Sylow | C3 ⋊ #65496 |
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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,d^2=f,b^a=bf,c^a=ce,h^a=h^4,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #14280969, #14280972, #14281000, … |
| maximal normal subgroup of | #14280969, #14280972, #14281000, … |
| maximal quotient of | #14280972, #14281003, #14281042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2700);