Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2054 |
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^46,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^46952 conjugacy classes — view the full character table.
| maximal subgroup of | #26102962, #26102964, #26102986, … |
| maximal normal subgroup of | #26102962, #26102964, #26102986, … |
| maximal quotient of | #26120070, #26120077, #26120154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5821);