Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #355 |
| Sylow | C5 ⋊ #4542 |
| Sylow | C3 ⋊ #64697 |
128 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 38 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|b^2=c,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,d^b=def,e^b=ef,g^b=g^2,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #14313574, D3×#64697, D5×#4542, … |
| maximal normal subgroup of | #14313574, D3×#64697, D5×#4542, … |
| maximal quotient of | #14277586, #14277676, #14278130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 207);