Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1540 |
256 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=e,c^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^46,d^b=dg,e^b=efg682 conjugacy classes — view the full character table.
| maximal subgroup of | #26107343, #26107346, #26107357, … |
| maximal normal subgroup of | #26107343, #26107346, #26107357, … |
| maximal quotient of | #26104217, #26104237, #26104563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3159);