Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | D4×Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3367 |
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^46,c^b=cg,d^b=de,f^c=fg604 conjugacy classes — view the full character table.
| maximal subgroup of | #26206101, #26206103, #26206161, … |
| maximal normal subgroup of | #26206101, #26206103, #26206161, … |
| maximal quotient of | #26232914, #26233099, #26235251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17228);