Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#473 ⋊ C2 |
| Sylow | C47 ⋊ #2194 |
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,h^b=h^46,e^c=eg391 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2194, C2×#20245357, #26370232, … |
| maximal normal subgroup of | D47×#2194, C2×#20245357, #26370232, … |
| maximal quotient of | #26128425, #26128435, #26128769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6479);