Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1969 |
312 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 117 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,b^2=df,c^2=eg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^461516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26103047, #26103049, #26133348, … |
| maximal normal subgroup of | #26103047, #26103049, #26133348, … |
| maximal quotient of | #26115136, #26115170, #26115434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5371);