Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #340 |
| Sylow | C5 ⋊ #4551 |
| Sylow | C3 ⋊ #64893 |
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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=c,b^2=de,d^2=f,b^a=bd,d^a=df,g^a=g^2,h^a=h^3,h^c=h^4108 conjugacy classes — view the full character table.
| maximal subgroup of | #14278173, #14278175, #14278184, … |
| maximal normal subgroup of | #14278173, #14278175, #14278184, … |
| maximal quotient of | #14276753, #14276799, #14276966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 959);