Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ #1819 |
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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,c^2=d,b^a=bd,c^a=ce,e^a=eg,f^c=fg,h^c=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26103650, #26108851, #26108882, … |
| maximal normal subgroup of | #26103650, #26108851, #26108882, … |
| maximal quotient of | #26109599, #26109605, #26109611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4582);