Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C47×#466 ⋊ C2 |
| Sylow | C47 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^46,e^d=eg,h^d=h^46541 conjugacy classes — view the full character table.
| maximal subgroup of | #26372729, #26372733, #26372739, … |
| maximal normal subgroup of | #26372729, #26372733, #26372739, … |
| maximal quotient of | #26205620, #26205631, #26205635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 16184);