Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C47×#343 ⋊ C2 |
| Sylow | C47 ⋊ #2078 |
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^46,c^b=cf,f^b=fg,h^b=h^46,e^c=eg,f^c=fg532 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2078, C2×#20244832, #26245184, … |
| maximal normal subgroup of | D47×#2078, C2×#20244832, #26245184, … |
| maximal quotient of | #26120982, #26120987, #26120992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5954);