Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C47×#379 ⋊ C2 |
| Sylow | C47 ⋊ #1781 |
880 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 109 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=f,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26103624, #26108847, #26108880, … |
| maximal normal subgroup of | #26103624, #26108847, #26108880, … |
| maximal quotient of | #26107604, #26107607, #26107614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4424);