Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #1534 |
196 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 69 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,b^2=f,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^b=h^46670 conjugacy classes — view the full character table.
| maximal subgroup of | #26108809, #26108810, #26108812, … |
| maximal normal subgroup of | #26108809, #26108810, #26108812, … |
| maximal quotient of | #26104357, #26104359, #26104395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3136);