Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1533 |
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 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,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^46,d^b=dg,e^b=efg670 conjugacy classes — view the full character table.
| maximal subgroup of | #26104004, #26104005, #26104046, … |
| maximal normal subgroup of | #26104004, #26104005, #26104046, … |
| maximal quotient of | #26104355, #26104367, #26104393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3134);