Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ #3165 |
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^46,d^c=dg,h^c=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26113786, #26113788, #26113822, … |
| maximal normal subgroup of | #26113786, #26113788, #26113822, … |
| maximal quotient of | #26216708, #26219669, #26220862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15057);