Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×#97 ⋊ C2 |
| Hall | C3×C5 ⋊ #329 |
| Sylow | C5 ⋊ #4464 |
| Sylow | C3 ⋊ #64684 |
140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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|b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^2,h^a=h^4,d^b=df159 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#329, C2×#11746285, D5×#4464, … |
| maximal normal subgroup of | D15×#329, C2×#11746285, D5×#4464, … |
| maximal quotient of | #14276638, #14276676, #14277158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 480);