Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C47×#381 ⋊ C2 |
| Sylow | C47 ⋊ #1782 |
612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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,c^2=g,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 | #26103626, #26108451, #26108460, … |
| maximal normal subgroup of | #26103626, #26108451, #26108460, … |
| maximal quotient of | #26107610, #26107618, #26107621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4427);