Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C47×#347 ⋊ C2 |
| Sylow | C47 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^46,d^b=dfg,e^b=eg,f^b=fg,h^b=h^46,d^c=dg529 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2180, C2×#20245281, #26369725, … |
| maximal normal subgroup of | D47×#2180, C2×#20245281, #26369725, … |
| maximal quotient of | #26128153, #26128159, #26128231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6403);