Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C47×#455 ⋊ C2 |
| Sylow | C47 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 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.
Polycyclic presentation:
2^7,47|b^a=bd,c^a=ce,f^a=fg,c^b=cg,e^b=efg,h^b=h^46,d^c=df,h^c=h^46,e^d=eg385 conjugacy classes — view the full character table.
| maximal subgroup of | #26137010, #26137012, #26137017, … |
| maximal normal subgroup of | #26137010, #26137012, #26137017, … |
| maximal quotient of | #26128324, #26128364, #26128492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6510);