Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ #3160 |
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | #26134829, #26134831, #26134844, … |
| maximal normal subgroup of | #26134829, #26134831, #26134844, … |
| maximal quotient of | #26216687, #26219610, #26219611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15022);