Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C47×#358 ⋊ C2 |
| Sylow | C47 ⋊ #2175 |
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^46,d^b=df,f^b=fg,h^b=h^46,h^c=h^46538 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2175, C2×#20245255, #26369584, … |
| maximal normal subgroup of | D47×#2175, C2×#20245255, #26369584, … |
| maximal quotient of | #26128020, #26128211, #26128212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6377);