Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #2099 |
214 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 89 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=d,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^46,f^c=fg676 conjugacy classes — view the full character table.
| maximal subgroup of | #26105307, #26105310, #26105314, … |
| maximal normal subgroup of | #26105307, #26105310, #26105314, … |
| maximal quotient of | #26121403, #26124188, #26124536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6068);