Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×C4×C5 ⋊ D3 |
| Sylow | C5 ⋊ (C2×S4)⋊C4 |
286 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5,2^2|b^2=c,b^a=bd,e^a=e^2,f^a=f^4,g^a=h,h^a=g,g^e=h,h^e=gh92 conjugacy classes — view the full character table.
| maximal subgroup of | #14513009, #14513017, #14513022, … |
| maximal normal subgroup of | #14513009, #14513017, #14513022, … |
| maximal quotient of | #14511961, #14511963, #14511966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6327);