Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | #26106818, C8×#13093938, #26106823, … |
| maximal normal subgroup of | #26106818, C8×#13093938, #26106823, … |
| maximal quotient of | #26104235, #26104238, #26104240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2826);