Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#470 ⋊ C2 |
| Sylow | C47 ⋊ #3054 |
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^46,c^b=cg,h^b=h^46,h^d=h^46400 conjugacy classes — view the full character table.
| maximal subgroup of | #26126427, #26126440, #26370175, … |
| maximal normal subgroup of | #26126427, #26126440, #26370175, … |
| maximal quotient of | #26198794, #26198822, #26198864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 14121);